A new method for determining critical currents in coils made of second-generation superconducting tapes is considered in the paper. The proposed approach is based on the joint solution of the integral equation of the electromagnetic field and the equation of state of the superconductor material, the critical current density in which is determined on the basis of the modified anisotropic Kim–Anderson model. Discretization of the equation system has been done by the collocation method. By means of the developed algorithm for solving the derived equations system, we calculated the critical current in coils used in inductive energy storage systems. A series of numerical experiments revealed the effect of significant degradation of the critical current in the coils compared to the declared parameters obtained for short samples of a superconducting tape