For problem of correcting mass matrix of finite element model of undamped structural systems, the desired mass matrix properties, including orthogonality relation, symmetry, positive semidefiniteness and sparsity, are imposed as side constraints to form mathematically the optimal matrix approximation problems. The solvability conditions for the problems are presented. Based on the cyclic projection method, numerical methods are proposed for solving the matrix nearness problems. Numerical results show that the proposed methods are efficient.