Algorithms for simulation of such types of Levy processes as square-root diffusion processes, compound Poisson processes, jump diffusion processes, stable Levy processes have been investigated in this paper. These algorithms were implemented as classes using S3 class system in R. Obtained simulation classes have been enriched by methods to plot trajectory, returns, kernel density estimator of the log returns for corresponding Levy processes. In the case of square-root diffusion process Monte Carlo procedure for pricing european call option has been performed, and obtained option prices have been compared with their counterparts calculated using exact formula for call option valuation, that is available in this case.