The method proposed in paper solves a convex minimax problem with a set of general constraints. It is based on a schema elaborated previously, but with constraints that can be projected on quite elementary. Such kind of problems are often encountered in technical, economical applied domains etc. It does not use penalty functions or Lagrange function – common toolkit for solving above mentioned problems. Movement directions have a stochastic nature and are built using estimators corresponding to target function and functions from constraints. At the same time every iteration admits some tolerance limits regarding non-compliance with constraints conditions.