  We study a class of Newtonian models for the deformations of non-magnetized
neutron stars during their spin-down. The models have all an analytical
solution, and thus allow to understand easily the dependence of the strain on
the star's main physical quantities, such as radius, mass and crust thickness.
In the first ``historical'' model the star is assumed to be comprised of a
fluid core and an elastic crust with the same density. We compare the response
of stars with different masses and equations of state to a decreasing
centrifugal force, finding smaller deformations for heavier stars: the strain
angle is peaked at the equator and turns out to be a decreasing function of the
mass.We introduce a second, more refined, model in which the core and the crust
have different densities and the gravitational potential of the deformed body
is self-consistently accounted for. Also in this case the strain angle is a
decreasing function of the stellar mass, but its maximum value is at the poles
and is always larger than the corresponding one in the one-density model by a
factor of two. Finally, within the present analytic approach, it is possible to
estimate easily the impact of the Cowling approximation: neglecting the
perturbations of the gravitational potential, the strain angle is 40\% of the
one obtained with the complete model.
