Present methods of modeling a continuum manipulator do not pay much attention to nonconstant elasticity along the length, such as tensile or bending stiffness. In this paper, we develop a modified constant strain model based on the constant internal wrench and piecewise constant elasticity assumption. Section length and section compliance, which are the inverse of section stiffness, are set as the section kinematic parameters, and internal wrench as the kinematic variable. The explicit error model and the identify matrix of these kinematic parameters are derived in the product-of-exponentials (POE) formula. Redundancy and identifiability are discussed based on the identify matrix. The parameters are identified by minimizing the pose error through a nonlinear optimization algorithm, and effectiveness of the calibration is verified through experiments. The work can be beneficial for improving the modeling accuracy of a general continuum manipulator with complex structures and material properties.