This paper presents analytic solutions of defection and their resonance diagrams for a uniform beam of infinite length subjected to an constant axial force and moving transverse load simultaneously. Steady solutions are obtained by a time-independent coordinate moving with the load. The supporting foundation includes damping effects. The influences of the axial force, the damping coefficient and the load velocity on the beam response are studied. The limiting cases of no damping and critical damping are also investigate. The profiles of the deflection of the beam are shown graphically for several values of the load speed, the axial force and damping parameters. Form the results, following conclusions have been reached. 1. The critical velocity .THETA.cr decreases as the axial compressive force increases, but increases as the axial tensile force increase. 2. At the critical velocity .THETA.cr the deflection have a tendency to decrease as the axial tensile force increases and to increase gradually as the axial compressive force increases. 3. In case if relatively small dampings, the deflection increases suddenly as the velocity of the moving load approaches the critical velocity, and it reachs its maximum at the critical velocity, and it decreases and become greatly affected by the axial force as the velocity increases further. 4. in case of relatively large dampings, as the velocity increases the deflection decreases gradually and it is affected little by the axial load.