Exact models of uniformly rotating strange stars, built of selfbound quark
matter, are calculated within the framework of general relativity. This is
made possible thanks to a new numerical technique capable of handling the s
trong density discontinuity at the surface of these stars. Numerical calcul
ations are done for a simple MIT bag model equation of state of strange qua
rk matter. Evolutionary sequences of models of rotating strange stars at co
nstant baryon mass are calculated. Maximally rotating configurations of str
ange stars are determined, assuming that the rotation frequency is limited
by the mass shedding and the secular instability with respect to axisymmetr
ic perturbarions. Exact formulae which give the dependence of the maximum r
otation frequency, and of the maximum mass and corresponding radius of rota
ting configurations, on the value of the bag constant, are obtained. The va
lues of T/W for rapidly rotating massive strange stars are significantly hi
gher than those for ordinary neutron stars. This might indicate particular
susceptibility of rapidly rotating strange stars to triaxial instabilities.