  We evaluate the fermionic Casimir effect associated with a massive fermion
confined within a planar (d+1) dimensional slab-bag, on which MIT bag model
boundary conditions of standard type, along a single spatial direction, are
imposed. A simple and effective method for adding up the zero-point energy
eigenvalues, corresponding to a quantum field under the influence of arbitrary
boundary conditions, imposed on the field on flat surfaces perpendicular to a
chosen spatial direction, is proposed. Using this procedure, an analytic result
is obtained, from which small and large fermion mass limits, valid for an
arbitrary number of dimensions, are derived. They match some known results in
particular cases. The method can be easily extended to other configurations.
