The article presents and evaluates a scalable algorithm for validating solutions of linear programming problems on cluster computing systems. The main idea of the method is to generate a regular set of points (validation set) on a small-radius hypersphere centered at the point of the solution under validation. The objective function is calculated for each point of the validation set that belongs to the feasible region. If all these values are less than or equal to the value of the objective function at the point under validation, then this point is the correct solution. The parallel implementation of the VaLiPro algorithm is performed in C++ through the parallel BSF-skeleton, which encapsulates all aspects related to the MPI-based parallelization of the program. We provide the results of large-scale computational experiments on a cluster computing system to study the scalability of the VaLiPro algorithm.