New technique is presented for modeling the total cross sections of electron scattering by Na, K, Rb and Cs atoms in the low and intermediate energy regions. The calculations have been performed in the framework of genetic programming ( GP ) technique. The GP has been running based on the experimental data of the total collisional cross sections to produce the total cross sections for each target atom. The incident energy and atomic number as well as the static dipole polarizability have been used as input variables to find the functions that describe the total collisional cross sections of the scattering of electrons by alkali atoms. The experimental, calculated and predicted total collisional cross sections are compared. The discovered functions show a good match to the experimental data.