Summary: In engineering, many problems can be reduced to solve the partial differential equations (groups) with numerical methods. Numerical methods for solving partial differential equations include the finite difference method, finite element method and finite volume method. The core concept of these methods is to discrete the differential equations into a linear system, and the numerical solution of the original equations is obtained by solving the linear system. In this process, the coefficient matrix of the linear system is usually vary large and sparse, occupying large amounts of storage space and making the linear system difficult to solve. In order to alleviate the problem, this paper studies the compression storage method for large sparse matrix, which only stores non-zero elements. The strategy can reduce storage space and avoid zero elements to participate in calculation. In particular, in the process of generation of coefficient matrix, the insert operation of non-zero elements can be finished in constant time with the orthogonal list. In the process of solving, the Compression Storage Row/Column (CSR/CSC) can save storage space and improve the solver efficiency significantly. In experiment, we adopt the finite difference method to solve Laplace equation and use the finite element method to compute the stress distribution of the cross-section of a ring. For the linear systems, we use the orthogonal list and CSR/CSC to store the coefficient matrix, and use direct and iterative methods to solve the systems. Experimental results show that the compression storage method can not only greatly reduce the memory space for structured and unstructured matrices, but also can significantly improve the efficiency of the solvers.