The breaking of a neutron star crust is believed to play a fundamental role in some astrophysical phenomena like glitches, flares and the emission of gravitational waves from isolated compact objects. However, there is still lack of systematic (and quantitative) studies of the crustal deformation under different types of loads, which can be induced by rotation, pinning of superfluid vortices into the crustal lattice and magnetic fields. We introduce a simple Newtonian model that allows calculating the displacements, stresses, and strains due to a chosen force on a self-gravitating, compressible neutron star (NS). The object under study is here divided into two layers, an inner fluid core and an elastic crust, but with our approach an arbitrarily large number of layers are possible. As a first case of study we introduce the polytropic relation $n=1$ as equation of state for the matter inside the NS and, considering rotation as the perturbating force, we study the impact of different adiabatic indexes (simulating different astrophysical scenarios) and mass on the calculated quantities. We obtain that small variation in the adiabatic index cause large variations in the response of the star, both in displacements and strains, and explain what is the physic behind this behaviour. Moreover, we show that the deformation of a NS due to rotation is larger for lighter stars. Finally, we calculate that the strain developed between two glitches is orders of magnitude smaller than the lowest expected breaking strain.