Theoretical analysis of the critical currents in solenoids wound with anisotropic superconductors was performed. The results of the numerical calculations indicate that applying the external magnetic field to the cylindrical coils which are made of anisotropic HTS tapes may lead to some increase in their critical current. Taking into account the angle dependence of the of short Bi(2223)Ag tape samples measured at 77 K we have shown how the external homogeneous magnetic field parallel to the axis of cylindrical symmetry influences the value of the coil's critical current. We also present the analysis of the influence of the external magnetic field on the change in position of weak turns in the winding. It is shown that determination of the magnet critical current represents mathematically the solution of a non-linear equation. The methods as well as the computer procedure enabling the evaluation of the coil's expected critical current and the location of the position of weak places in the winding are described. Further, the expressions that can be applied to the calculation of critical currents of the magnets, made of superconducting wires and tapes, whose characteristics are isotropic, were derived. The possibility of obtaining analytical solutions for simplified linear and for the general case of is also discussed.