The present study analyzes the propagation of surface waves on a strongly inhomogeneous loaded bi-elastic cylindrical tube with variable material constituents. More precisely, due to the number of related physical applications, the exerted load is considered to be in favor of the Winkler elastic foundation. Further, analytical and approximation procedures of solution are beseeched to examine the model. The revealed results by two approaches are then graphically portrayed, which are then found to possess a high level of conformity. Finally, both the external load due to Winkler foundation d, and the internal material property b are found to oppose the propagation of surface waves in the media. In fact, the opposition deteriorates when both the dimensionless parameters d and b are greater than 0.5.