An alternative to the commonly employed Laplacian grid generation scheme for finite element problems is developed. The procedure is based upon a local quadratic isoparametric transformation. The proposed isoparametric generation scheme overcomes the one serious defect of the commonly used Laplacian scheme, i.e., the inability to significantly utilize boundary curvature information and boundary node point spacing information when locating interior nodes. In addition, a generalized generation scheme is given that includes the Laplacian and isoparametric schemes as special cases of a family of generation schemes; this family is defined by a parameter with a range of zero (Laplacian grid) to one (isoparametric grid). Examples are given which compare grids generated for various values of the parameter.