ABSTRACT: The essential features with high order DDA approaches exist in the fact that coefficients of complete polynomials are unknowns with which its governing equations are established on the rules of classical mechanics and that the simplex integration gives an analytical solutions of polynomial bases over volume of blocks. Based on high order polynomial displacement function in DDA and the Weierstrass theory for polynomial approximation, this paper presents a method approximating the continuous displacement function in continuous elastic media with complete and high order polynomials. Following contents are included which consist of complete and high order polynomial function and its strain matrix derivative in three dimensions, establishment for simultaneous equations for one block and block system where connecting faces are employed as to divide complex structure into blocks with simple shape, simplex integration introduction especially the recursive simplex integration formula, contacts and iteration solution of equilibrium equations of block system etc. At last, a case validation with a cantilever under bending is carried out. It has been primarily shown that case study gives a convergent solution and the idea with complete and high order polynomial approximation to continuous elastic mechanics analysis is acceptable. In other words, the DDA method may supply us another way to solve continuous elastic mechanics analysis with sufficient precision by obtaining a complete and high order polynomial displacement function as its displacement approximations.