TL;DR:

A Man express emotions, but in masculine ways:

• with outcome independence, and without neediness, nor seeking validation or comfort

• in subordination to his honor, values, reason, goals, and mission

• and only in accordance with his desires, values and mission

Emotional STFU for beginners.

Just as career betas who habitually run at the mouth and DEER every time they speak generally need a period of STFUing to learn to control these tendencies, feminized, emotionally needy males who habitually express emotions seeking validation, sympathy, reassurance and comfort will likely need a period of "emotional STFU" in which they learn to overcome this neediness. While often a necessary first step, (as with STFU) this is only a beginner's stage. The fully realized masculine Man openly and confidently expresses his emotions, as and when appropriate, in service of his goals, missions, values, and desires.

Emotions are OK

Many newbies seem to think that an alpha man should show no emotion. This is not true; nobody admires or loves a seemingly emotionless robot. Rather, masculine Men have strong emotions, but express them in masculine ways.

Others think that Stoicism involves suppressing all emotion, like Mr. Spock from Star Trek. This is also incorrect; most branches of Stoic thought emphasize mastery and subordination of emotion, rather than its elimination.

A Man expresses emotion with Outcome Independence (OI), and never for validation, sympathy, or forgiveness.

Sexual desire is a strong emotion, and MRP advocates open expression of sexual desire (that is, flirt, game, and initiate often and overtly). The key for alpha men is to express this emotion with OI. The exact same rule holds for the expression of any emotion by a Man.

The flip side of this rule is that a Man never expresses emotion out of neediness. A Man is emotionally self-sufficient, and needs no emotional validation, sympathy, or forgiveness. As perceptively noted by /u/logger1234, beta males typically say "I love you" to elicit a reassuring "I love you too." An alpha says it because he desires to express his feelings, and requires no response. Women comfort test to seek reassurance; comfort or reassurance seeking behavior in adult males is extremely unattractive. Children and women may cry to elicit sympathy or forgiveness; a Man does not. He may cry at, say, the death of his beloved mother or father, but as an open expression of his sadness, not as a covert request for sympathy from others.

A Man subordinates his emotions to his honor, values, reason, goals, and mission.

A Man will fight rather than grovel in fear. A married Man whose values include fidelity to his marriage vows declines opportunities to cheat. A Man works toward his missions and goals through anger, frustration, discouragement, or sadness.

A Man expresses his emotions only in accordance with his desires, values and mission.

A Man expresses his emotions to serve his goals, rather than being a slave to his emotions. He STFU's when expressing his emotions does not serve his current goal.

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Fun Study Guide: Classic redpill movie example

In the classic movie The Maltese Falcon, the ultimate alpha (detective Sam Spade as played by Humphrey Bogart) uses his superior frame and often machiavellian expression of his emotions to singlehandedly outmaneuver a world of lesser alphas, betas, and manipulative women to turn an initially desperate situation into a total victory for himself. (The Maltese Falcon is an object lesson in frame, and the masculine expression and use of emotion; all men who wish to master frame or appropriate emotional expression should study this movie carefully.)

In a dramatic scene in The Maltese Falcon, Sam Spade feigns extreme anger with Gutman as a negotiating ploy to get Gutman to reveal needed information, shouting "you'll talk to me today or you're through. What are you wasting my time for? I can get along without you!" (OI) In this scene, Spade also accepts the significant danger of provoking the gunsel. In other scenes, Spade risks being punched or arrested when angrily provoking the police Lieutenant to make him back off. In the dramatic denouement, Spade admits his love for Brigid, but her response doesn't matter; he has already decided her fate. Spade's complete willingness to accept whatever consequences may come (OI) from his open expression of his emotions makes him the dominant alpha.

In spite of his love for Brigid, Spade handed her over to the police to avenge the murder of his partner (honor, values, goals, mission). He also knew he could never trust her (reason). In the dramatic glass-breaking scene with Gutman, Spade overcame his fear (as revealed by his trembling hands afterwards) to fake his angry outburst to convince Gutman to deal with him.

Spade never reveals his fear of his opponents to them, even though he clearly feels fear at times, because doing so would compromise his mission of solving the case. He hides his fear of being arrested to the police, but he expresses this fear to Gutman, Cairo, and the gunsel to turn them against each other. He boldly expresses his anger when it is beneficial to do so, and hides it when it is not. He hides his desire for Brigid for much of the movie, then kisses her to gain her confidence at a strategic moment. He reveals his love for her only after he has solved the case and decided her fate, and only because he desires to explain his decision at a time when it is safe to do so.

Edit: Added TL;DR and reorganized.