The stability of the cracked visoelastic rectangular plate of varying thickness subjected to uniformly distributed tangential follower force is investigated. Two models describing thickness variation are parabolic and linear variations along one edge of the plate. This is done in order to show how critical loads for cracked visoelastic thin plate subjected to follower force can be obtained using the two-dimensional viscoelastic differential constitutive relation and the thin-plate theory. The differential equations in the Laplace domain are established. The complex eigen-value equations are derived by the differential quadrature method. The generalized eigen-value under different boundary conditions is calculated. The effects of the plate parameters, the crack parameters and the dimensionless delay time on the stability of the viscoelastic plates are analyzed. The crack is found to change the type of instability and reduce the stability of varying thickness viscoelastic plate.