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The goal of this paper is to demonstrate the introduction of dimensional variables as well as the applications of dimensional analysis in Computer Algebra system (Mathematica). The package Dimensional Analysis developed by author uses nondimensionalization based on II-theorem to simplify equations and to reduce the number of parameters when the governing equations are not known. The package contains symbols, dimensional formulae and units for principal physical quantities, as well as a number of named dimensionless parameters. Another important feature of the package is its ability to check the dimensional homogeneity of the expressions. This package is aimed at helping researchers with the preliminary analysis of models and simplification of large-scale problems by using dimensionless parameters. The package can also be used in teaching.