This paper presents an analytical model for calculating the workspace of a flexure-based hexapod nanopositioner previously built by the National Institute of Standards and Technology (NIST). This nanopositioner is capable of producing high-resolution motions in six degrees of freedom by actuating linear actuators on a planar tri-stage. However, the workspace of this positioner is still unknown, which limits its uses in practical applications. In this work, we seek to derive a kinematic model for predicting the workspace of such kinds of flexure based platforms by assuming that their workspace is mainly constrained by the deformation of flexure joints. We first study the maximum deformation including bending and torsion angles of an individual flexure joint. We then derive the inverse kinematics and calculation of bending and torsion angles of each wire flexure in the overall mechanism with given position of the top platform center of the hexapod nanopositioner. At last, we compare results with finite element models of the entire platform. This model is beneficial for workspace analysis and optimization for design of compliant parallel mechanisms.