A numerical study of combustion in bidirectional swirling jets arrays is performed for the first time. A choice of bidirectional flow for designing burner arrays is caused by their advanced properties in terms of combustion stability, long fuel residence time, pollutants emission, etc. The simplest array studied in the paper is of square shape (3 × 3) and consists of the central toroidal bidirectional chamber and 8 peripheral cylindrical chambers. Such a decision is made to improve the stability of combustion due to the advantages of the toroidal shape known from the previous studies. The main result for the square array is that the flame surface area increases significantly, and the fuel burning rate is 1.68 times more compared to a single bidirectional chamber. Additionally, the simulations show that the key factor in array combustion stability is related to the formation of central recirculation zones in each bidirectional jet. Based on these results, the multipoint gas turbine combustor is designed. Its primary combustion zone is formed using the multiplied 3 × 3 array of bidirectional jets over the annulus. Thus, the overall number of simple vortex chambers in the annular array is 90. A numerical simulation of the new multipoint combustor operation shows a very intense jets interaction in its first half and its efficiency is more than 99%. Moreover, the calculated emission properties at an overall pressure ratio OPR = 40 suit the modern environmental requirements: CO = 12 ppm, NO = 22 ppm.