The work is devoted to the selection of optimal conditions for the synthesis of anisotropic gold nanoparticles, which can be used in solar energy, catalysis, chemical sensors and in medicine, where it is offered to carry out the diagnosis and therapy of cancer patients with their help. The mathematical model is obtained. It reflects the influence of reaction parameters in the synthesis of gold nanoparticles bipyramidal form. We found optimal conditions to form the bipyramid of gold with size about 76х24 ± 5 nm and  long-wave maximum of the LSPR at 870 nm. Also we optimized a technique to obtain gold nanorods with different axial ratio and the position of the wavelength maximum of the LSPR in the range of 730÷850 nm. The obtained nanorods have dimensions about 29х6 ± 1.5 nm, 20х5 ± 2.5 nm and 23х7 ± 1 nm, confirmed by transmission electron microscopy.