Small punch test (SPT) has been widely used to evaluate in-service materials in nuclear fusion facilities. Early use of SPTs is largely based on empirical relations or curve fitting from experimental data, while recent applications of SPTs take advantage of finite element methods. In this study, an improved inverse finite element analysis procedure is proposed to obtain constitutive relations from load-displacement curves recorded in SPTs. In addition, a parametric study is performed to evaluate the effects of SPT parameters including friction coefficient, punch head diameter, sample thickness, specimen scale and boundary conditions. The proposed inverse finite element (FE) method improves the accuracy of existing inverse FE methods, and the current parametric study provides a basis for the standardization of SPT procedures in the future.