The paper discusses the use of parallel computing on a central processing unit (CPU) to solve the forward kinematics of a parallel hexapod robot. The paper proposes two algorithms to solve the forward kinematics. The first is based on the direct use of the system of equations of kinematic relations of the mechanism. The approximation of a set of system solutions represents a problem of a nine-dimensional grade. The second approach is based on the approximation of a set of solutions to the system of inequalities of a three-dimensional grade. A software package for implementing the proposed algorithms was developed. The comparative analysis of the effect of parallel computing on the speed of the presented algorithms was carried out.