The etch-induction time, Tc, is measured for α-particles in CR-39 plastic track detector and the etch-critical time, Tc, is calculated for α-particles in CR-39 detector as a function of α-energy, E, and incident angle, 0. The etch-induction time was found to be independent of dip angle and directly proportional to the α-particle energy in the range from 1–6.1 MeV. The etch-critical time was found to be zero for angles greater than the critical angle, 0c, whereas at angles less than 0c, the etch-induction time, Ti, was increased by the value of Tc.