AbstractFor a wide calss of finite element matrices integrated numerically rather than exactly, a definable number of sampling points is found to be sufficient for keeping their theoretical properties unchanged. A systematic criterion limiting the number of possible point configurations for numerical quadrature formulas on triangles is established. Some new high order formulas are presented. Tables containing optional formulas with respect to minimum number of sampling points and required degrees of accuracy are given. They are arranged so as to assist with selection of suitable quadrature formulas for finite element computer programming.