  Considering a massive or massless free spinor field propagating in a flat
five dimensional space with its fifth dimension compactified either on a strip
or on a circle, we analyse the procedure of generation of the four dimensional
Kaluza-Klein spinor mass towers. Requiring the five dimensional Dirac operator
to be symmetric, the set of all the allowed boundary conditions is obtained. In
the determination of the boundary conditions and in the Kaluza-Klein reduction
equations, the SO(3,1) and parity invariances in the space-time subspace are
carefully taken into account. The equations determining the mass towers are
written in full generality. A few numerical examples are given.
