In contacts of functionally graded elastic solids, the conditions produced are significantly different from the ones in similar contacts of homogeneous elastic materials. Especially it is true for heavily loaded lubricated contacts. The situation is even more diverse due to different dependences of the material elastic parameters on material depth. In the previous papers, the cases of lubricated contacts with coatings made of homogeneous materials are considered using asymptotic and semi-analytical methods. The goal of the paper is to determine the behavior of the coating effectiveness criteria in heavily loaded elastohydrodynamically lubricated (EHL) contacts for coatings with elastic modulus varying linearly and exponentially across the coating thickness as well as to compare the results with the case of coatings made of homogeneous materials. The above criteria include the criteria on the lubrication film thickness and friction force. The approach used for analyzing the influence of functionally graded elastic materials on parameters of heavily loaded line EHL contacts is based on the asymptotic methods earlier developed by the authors. The analysis is based on splitting the problem into two distinct parts: the problem for dry (nonlubricated) contacts and a problem for lubricated contacts. The bridge between the two problems is the asymptotic behavior of pressure in the vicinity of the end points of the contacts. More specifically, in the central part of the contact the solution of the EHL problem for functionally graded materials is close to the one for the dry contact of these materials while in the narrow zones near the inlet and exit points of the contact the lubrication effects become comparable to the effects due to the elasticity of the solids. This approach to the EHL problem solution reveals its structure.