The symbolic matrix method which gives compact representation and efficient determination of expressions for the Hamiltonian and other matrix operators arising in configuration interaction (CI) calculations is presented. With this method, the computing and storage requirements for matrix expressions become insignificant compared to the total requirements of a CI calculation. The efficiency is achieved by taking advantage of analogies between expressions of different matrix elements to reduce drastically the number of expressions determined explicitly. The symbolic matrix method is completely general, unrestricted by the type of operators considered, or by the choice of n-particle basis. It can take full advantage of any point group symmetry, and the ordered interacting spaces to reduce the dimension of the n-particle basis. In addition, the method provides a basis for a general direct CI method which will be presented in a forthcoming paper. A comparison with the graphical unitary group approach is provided. © 1981 American Institute of Physics.