The purpose of this study is to develop methods for numerical optimization and sensitivity analysis of pultrusion process parameters. With this objective in mind, a mathematical model of material behavior is implemented within the ABAQUS environment, accounting for the dependence of matrix thermomechanical characteristics on temperature and degree of polymerization, the rate of chemical reaction of thermoset matrix polymerization, and thermal and mechanical contact with a die. Modeling methods developed describe a temperature field distribution, a degree of curing and a stress-strain state in a during pultrusion process. For numerical optimization and sensitivity analysis of process parameters the special simulation scheme was developed using pSeven software suite. pSeven is a platform for automation of engineering simulation and analysis tasks, multidisciplinary optimization and data mining. As an example, the pultrusion of glass-fiber reinforced C-section profile used in bridge construction is presented. The optimization parameters are the initial temperature of the resin, temperatures in die zones 1 and 2, and the pulling speed. The constraints are the transverse stress in the pultruded profile, maximum temperature of the material, and a degree of cure at the end section. Objective functions of two-criterion optimization are the pulling speed and the maximum spring-back at the end section. Total computing budget of the problem is 80 points. The study of an approximation model has been conducted and constraints have been investigated. Pulling speed increase of 18 % has been achieved, satisfying all constraints. Pareto-front of optimum configurations in two-criterion problem has been obtained.