Based on Biot's basic motion equations for the fluid saturated porous elastic medium and by using the method of complex function,the displacement field due to moving source with uniform velocity U in an infinite porous elastic saturated space is studied in present paper,Two types of sources are considered:a.An oblioue concentrated pulse force moving along the horizontal axis of the infinite space,b.The moving couples of forces.There are four cases for the moving velocity of force source:a.The velocity U is less than all three types of body wave velocities of the fluid saturated porous elastic medium,the subsonic case.b.The velocity U is less than the first dilatational wave velocity and the rotational wave velocity of the medium,but greater than the second dilatetional wave velocity,the weak transonic case.c.The velocity U is less than the first dilatational wave velocity,but greater than the velocities of the second dilatational and the rotational waves,the strong transonic case.d.The velocity U is greater than all three types of body wave velocities,the supersonic case.The results show that in the transonic and supersonic cases,the solutions represent the character of plane chock waves attached to the load and associated with a jump in the displacement.