CR-39 and LR-115 type II solid state nuclear track detectors (SSNTDs) are both used, in order to assess the concentration of nucleus belonging to 238U and 232Th series, these ones can be also used to measure radon 222Rn and thoron 220Rn gases in different locations. In this paper, a Monte Carlo code was developed to calculate the mean critical angle for which alpha particles emitted from 238U and 232Th families in studied material samples reach CR-39 and LR-115 type II surfaces and bring about latent tracks on them. The dependence of the SSNTDs mean critical angle on the removed thickness, the initial alpha particle energy has been studied. A linear relationship between CR-39 mean critical angle and the initial alpha particle energy for different removed thicknesses has been found. This straightforward relationship allows determining quickly the mean critical angle of etching which corresponds to initial alpha particle energy for a given removed thickness. CR-39 mean critical angle ranged from 59° for an alpha particle emitted by 212Po to 71° for an alpha particle emitted by 232Th, for the value of removed thickness of 6 µm; whereas LR-115 type II mean critical angle does not depend on the initial alpha particle energy except for 232Th, 238U, 230Th and 234Ra when the removed thickness ranged from 6 µm to 8 µm. Obtained data by using the current method and those obtained in the literature  are in good agreement with each other.