AbstractModifled Simplex Search Procedure (MSSP) is amodification- generalization of the Nelder a nd Mead simplex method (NMSM). In MSSP, more than one vertex can be reflected ; and the techniques handling reflection, expansion ,contraction, and shrink age in this situation have been successfuIly developed, The number of vertices to be reflected is a functionofη, a new parameter . By specifying a sufficiently large value (maximum effectiveηor larger) for this parameter , MSSP reduces to the Nelder and Mead algorithm.The MSSP algorithm with a recommendedηvalue proves to be superior to NMSM and, in high dimensional cases ,to the Fletcher and PoweIl variable metric method (FPVM).The pro posed method MSSP is unique in that it is a direct search method particularly good for high dimensional problems and is suitable to be inc1uded in an oottmtzation package because of its capability to search in complicated terrain, its different style of searching, and its smaIl program size.