In order to solve integrating nesting and routing problem arising in computer-aided manufacturing for computer numerical control sheet cutting equipment the algorithm based on multi-contour cutting with common cut is proposed. The application of special cutting techniques (for example, common cut, chained cutting, snake cut) results in reducing values of cutting parameters; therefore, the proposed algorithm is based on multi-contour cutting. As a result of multi-contour cutting application the material consumption and cutting cost are reducing. As standard parts we consider triangles with inner/outer contours. Algorithm consists of two base steps. At the first step, the automatic nesting of standard parts on sheet material is performed. The input data is *.dxf file with geometry of part and value n , which is required number of parts. The part vertex coordinates are extracted from *.dxf file, and calculation of the following part vertex coordinates is performed. Based on calculation of the vertex coordinates the new *.dxf file as a nesting result is created. The visualization of nesting result is performed. The parts are nested with common cut. At the second step, the routing path of cutting tool is calculated for the resulting nesting according to the previous step of the algorithm. Algorithm implementation is performed in Python. The results of standard examples of numerical calculation for computer numerical control of laser sheet equipment are given.