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 most contexts, biceps and triceps are usually treated as plural, and bicep and tricep have become the conventional singular forms. This is the case outside scientific and medical writing, anyway.
Examples
In most types of writing, biceps and triceps can be either singular or plural—for example:
[H]e 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, use of these words is widespread. For example, the forms appear in these edited publications:
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]