The results of experimental and theoretical studies of collisional ionization of Na Rydberg atoms in nS and nD(n ≤ 8-20) states are presented. Molecular and atomic ions from associative ionization and photoionization by blackbody radiation were detected after pulsed laser excitation of Rydberg states in crossed Na atomic beams. An original method of determination of associative ionization rate constants based on the measurement of ratios of molecular and atomic ion signals was used, which did not require the determination of absolute number density of Rydberg atoms. The measured rate constants of associative ionization of Rydberg atoms in collisions with ground-state Na atoms are compared with the results of our earlier single-beam experiment and theoretical calculations. It is shown that the stochastic ionization model, which describes the collisional ionization of Rydberg atoms in terms of chaotic migration of highly excited electron induced by the motion of the colliding nuclei, yields a significantly better agreement with the experimental results than the earlier Duman-Shmatov-Mihajlov-Janev model.