Currently, for numerical simulation of random processes two types of the random number generators are used. The first type is based on the algorithmic methods for generating pseudorandom numerical sequences. The second type of generators is based on the use of physical sources of noise or of chaotic processes. The first type of generators does not permit to obtain the truly random numerical sequences, and the second type generators are used to form a truly random numerical sequence. In this paper, the possibility of creating promising generators of random numerical sequences of the second type, based on silicon photo-electronic multipliers with p - p-n - and n - n-p -structures by applying the pulsed optical radiation to these photo-detectors, has been shown. Using the experimental setup the influence of the supply voltage, optical radiation parameters, and, also, the parameters of the recording equipment, has been evaluated. The recommendations for choosing the values of the energy exposure of optical pulses, the overvoltage and the amplitude selection threshold, the implementation of which ensures that the generated random numerical sequence complies with the NST (National Institute of Standards and Technology) standard, have been formulated.