It can be difficult to find synonyms for the phrase "erect penis" without relying on vulgar or crass language. Some more polite options include "stiff member," "firm phallus," "rigid organ," or "hard shaft." Other possibilities include "turgid appendage," "tumescent member," or "engorged phallus." However, it's worth noting that using euphemisms or indirect language in discussions about sexual health can be limiting and problematic. In medical contexts, it's important to use clear and direct language to help patients understand their bodies and their options for treatment and care.