Due to increasing speed and mass of trains and vehicles, the errors arising from utilizing moving force method to obtain dynamic response of bridges cannot be neglected. In this paper, dynamic response of bridges under moving loads is studied. The bridge is modeled as simply-supported Euler-Bernoulli beam. Since in modeling moving loads by moving force method, inertial forces are neglected, this method is valid for a limited range of influential parameters (speed and mass). By considering inertial forces between the moving load and supporting structure, moving mass method can be utilized to extract dynamic governing equations. Numerical results reveal that by increasing speed and mass of the moving load, midpoint dynamic deflection of bridge obtained by two distinct methods differ considerably.  For example, for mass ratio of 0.15 and speed ratio of 0.8, 11 percent difference is observed in midpoint dynamic deflection calculated by two aforementioned methods.