In cheese-like products, milk components (in particular fat) are partially or completely replaced with non-dairy substitutes. An attempt was made in this study to determine whether Edam-type cheese can be distinguished from its substitute, where milk fat was replaced with palm oil, based on rheological properties. The rheological properties of Edam cheese and its substitute were analyzed during a 16-week ripening period, based on the results of a stress-relaxation test. The values of the rheological parameters were estimated with the use of the generalized Maxwell model and a non-linear model proposed by the authors, which accounted for the plastic deformation of the analyzed samples. The study revealed that both methods were equally effective in describing the stress relaxation process; therefore, they can be regarded as equivalent. Excluding the initial stage of ripening (which is not important from the consumers' point of view), the replacement of milk fat with palm oil did not influence the rheological properties of Edam-type cheese and the cheese-like product. In subsequent stages of ripening, no significant differences were found in the rheological properties of both products, which could only be used to evaluate their ripeness.