A flow field constructed by the superposition of a rotation and a simple shear Bow contains a small particle. A shear induced lift force acts on it. The equations of motion of the particle, which include this lift force, are solved using a singular asymptotic expansion. Conditions are obtained under which the effect of the lift force on the trajectory of the particle leads to instability. It is shown that even when the instability is not attained, and the lift coefficient is much smaller than the critical one, the effect of the shear induced lift may still be quite large. An example of turbulent flow in a pipe demonstrates the appreciable effect of the lift force on the path traced by the particle.