Biceps and triceps—each denoting a type of muscle—are singular nouns that look like plurals. Bicepses and tricepses are the logical plurals, but they’re only rarely used. In real-world usage, biceps and triceps are usually treated as plural, and bicep and tricep have become the conventional singular forms. Unless you’re writing a scientific text, these nontechnical singular forms are fine.
Examples
Biceps and triceps can be either singular or plural—for example:
… he tried to smack a delivery from Sajid Mahmood so hard that his biceps was torn off the bone. [Guardian]
His biceps are bigger than the thighs of many mere mortals. [Salt Lake Tribune]
His injured right triceps is healing, but continued hard shots could delay the process. [News Herald]
Jeff is struggling on his skis; his triceps are sore. [New York Magazine]
And though biologists may bristle at bicep and tricep, usage of these words is widespread. For example, these writers have no qualms about using the questionable forms:
But at least one method, hormone implants, visibly bulge from a man’s bicep. [New York Times]
His physique is that of a man, more mature than 17, a tattoo peeking out from one bicep. [Irish Times]
Tsonga said he was bothered by “general tiredness” in his right bicep … [Toronto Star]

