Abstract: Small deformation problems of pre-stressed bar are studied in present paper. Regarding initial stresses as parameters, a variational principle of displacement is suggested. Numerical parameters are used to describe initial stress. Based on the variational principle, a mathematical system of equations to solve displacement components of the bar is established. Numerical parameters are contained in the obtained equations. The system of equations is suitable for dynamic analysis of stressed members including pre-stressed bars on that small deformations are superposed. Analyzing the mathematical system, it is observable that the stiffness, critical force, couple of elemental deformations and inherent frequencies are affected by the numerical parameters.