We consider the problem of integrated sensing and communication (ISAC) involving a massive number of users in an unsourced random access (URA) system, called unsourced ISAC (UNISAC). In UNISAC, there are two sets of communication and sensing users that transmit signals in a random-access way. Hence, the received signal of each user is heavily corrupted by interference from numerous other users, making it challenging to extract individual transmissions. UNISAC is designed to decode the message sequences from communication users while simultaneously detecting active sensing users and estimating their angles of arrivals, regardless of the senders' identities. We propose a practical model for UNISAC that demonstrates the feasibility of the approach, achieving performance comparable to—or even surpassing—known ISAC results in certain regimes while being lower in others.