The simplex integration formula presented by Genhua Shi gives analytical solution and is widely used in the discontinuous deformation analysis and the numerical manifold method. Based on the special matrix operations including Kronecker product, Hadamard product and vectorization, the integration of monomial integrand on simplex domain is expressed in matrix form and a recursive formula for the simplex integration is presented. Compared with Shi’s integration formula, the recursive formula requires much less computation and incidentally obtains the integrals of all lower order integrands at the same time of computing integration of high order integrand. 