In this paper, a stochastic adaptive method with the ε-projection for stochastic gradient has been developed to solve two-stage stochastic linear problems. The method is based on the adaptive regulation of the size of Monte-Carlo samples and a statistical termination procedure taking into consideration the statistical modelling accuracy. To avoid “jamming” or “zigzagging” in solving the constraint problem the procedure for stochasticgradient epsilon-projectionhas been implemented. Four algorithms of the epsilonprojection are tested by the computer simulation. The recommendationsto solve two-stage stochasticlinear problems are made under the numerical study and results of solving the test examples.