The analysis of Pre-stressed Euler-Bernoulli beam traversed by uniform partially distributed moving mass is carried out. Equations of motion are solved systematically which results to the use of finite difference algorithm. Results from the numerical solution are shown graphically. It was observed that amplitude deflection of the moving mass Pre-stressed Euler-Bernoulli Beam was greater than those of the moving force. Also the moving force is not an upper bound for the accurate solution for the moving mass problem.