  The magnetoresistance (MR) of SrTiO$_3$ is theoretically investigated based
on the Boltzmann equation by considering its detailed band structure. The
formula for MR proposed by Mackey and Sybert is extended to be applicable to a
system with an arbitrarily shaped Fermi surface. It is shown that the angular
dependence of the diagonal component of the mass tensor causes transverse MR,
whereas that of the off-diagonal component causes longitudinal MR with only a
single closed Fermi surface, which overturns the textbook understanding of MR.
The calculated MR (300% at 10 T) quantitatively agrees with the experimental
results for SrTiO$_3$ including the behavior of the linear MR. The negative
Gaussian curvature of the Fermi surface of SrTiO$_3$ and its resulting negative
longitudinal and transverse MR are also discussed.
