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Fused Deposition Modeling (FDM) is one of the most used 3D technology for rapid prototyping of different parts. The approach consists in determination of the statistical significance of different parameters using the Analysis of Variance (ANOVA) technique followed by the determination of the correlation laws between the input and output data. These laws are usually described by polynomials obtained with the aid of the Least Squares Method. The use of this method is preferred due to its simplicity, but it has the disadvantage that the error is not known (the only thing we know is that the obtained polynomial leads to the smallest error in the sense of the Least Squares). In our paper we purpose a new approach by using the Tchebyshev polynomials which lead to the mini-max approximation of the law. In this way, the error is always zero in the division points and, moreover, the great advantage is that the error is the smallest one for the entire interval of the input data. The theoretical difficulty of this approach consists in the determination of the division points, while the practical disadvantage is the use of irrational division points for the input data. The formula obtained for the law of variation of the output with respect to the input is the most accurate one in the class of certain polynomials.