  We propose a spherically symmetric and anisotropic model for strange quark
stars within the framework of MIT Bag model. Though the model is found to
comply with all the physical requirements of a realistic star satisfying a
strange matter equation of state (EOS), the estimated values the Bag constant
for different strange star candidates like Her X-1, SAX J 1808.4-3658 and 4U
1820-30, clearly indicate that the Bag constant need not necessarily lie within
the range of 60-80 MeV fm$^{-3}$ as claimed in the literature.
