The simplex integration is commonly used in the numerical manifold method (NMM) for accurate integration. But a difficulty is encountered in adopting the simplex integration in high -  order NMM sInce all integrands have to be explicitly expressed in polynomial functions. To determine the explicit form of integrands, the formulation of element matrices of high -  order NMM is derived by using the special matrix operations including Kronecker product, Hadamard product and vectorization , resulting in a convenience of the derivation of the element matrices and  the explicit expression of integrands. Based on the derived formulae, a program of 3 - D NMM with high -  order for elastic static analysis of continuum is developed  and verified by examples.