We present a high precision Monte Carlo study of the spectrum of the Z
(2) gauge theory in 2 + 1 dimensions in the strong coupling phase. Usi
ng state-of-the-art Monte Carlo techniques we are able to accurately d
etermine up to three masses in a single channel. We compare our result
s with the strong coupling expansion for the lightest mass and with re
sults for the universal ratio sigma/m(2) determined for the phi(4) the
ory. Finally the whole spectrum is compared with that obtained from th
e Isgur-Paton flux-tube model and the spectrum of the 2 + 1-dimensiona
l SU(2) gauge theory, A remarkable agreement between the Ising and SU(
2) spectra (except for the lowest mass state) is found.