The grey system theory is a method which is used in situations when various assumptions are not valid in the application of parametric statistical analysis methods. The grey relational analysis is one of the subtopics of the grey system theory and defined as the grading, categorization and decision-making in the data set by using the Grey Relation Coefficient (GRG). In this study, the sensory analysis results of the samples obtained from the Longissimus Dorsi (LD), triceps brachi (TB) and semitendinosus (SMD) muscles of the Awassi and Red Karaman sheep breeds were tried to be researched by using the Grey Relational Analysis together with which ones were more preferred in terms of breed and muscle type. At the end of the study, no difference was observed between the preferability degrees of the Awassi (GRG=0.589) and Red Karaman (GRG=0.595) breeds. It was found that there was no important difference between the muscles as per the GRG relation coefficient, but the most preferred muscles were SMD (0.607), LD (0.589) and TB (0.578), respectively. It was determined in the sensory analysis made within this study that the most important factors distinguishing the preferability status of the mutton were WBS (0.729), juiciness (0.658), tenderness (0.581), NCBS (562), flavour (0.532) and acceptability (486), respectively.