Replacing and selecting materials for different engineering applications is relatively common. It must be noted that in some cases, there is more than a single definite criterion for selecting the right kind of material. The designers and engineers have to take into account a large number of material selection criteria. Experts usually apply trial and error methods or build on previous experimentation. In this paper, a new approach has been carried out for the use of the ELECTRE: ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing the REality) model in material selection. By producing a material selection decision matrix and criteria sensitivity analysis, ELECTRE has been applied to obtain a more precise material selection for a particular application, including logical ranking of considered materials. A list of all possible choices from the best to the worst suitable materials can be obtained taking into account all the material selection criteria, including the cost of production. This work shows that ELECTRE can be used successfully in selecting a suitable material for the particular application of a loaded thermal conductor. There is good agreement between the results of the methods being used and available data in Cambridge Engineering Selector (CES) databases. A computer program, Mathematica has been developed to facilitate the application of the method to other types of material selection problems.