Electrical machines often utilize stranded parallel conductors to reduce the skin-effect losses. This practice can lead to uneven total current distribution among the strands, increasing the resistive losses. Direct finite-element (FE) analysis of circulating current problems can be computationally costly due to the large number of nodal unknowns in the FE mesh in the conductor domains. Methods to reduce the computational burden exist for special problems only. This paper proposes two efficient FE formulations to solve the circulating current problems with arbitrary winding configurations. According to simulations, the proposed methods yield reasonably accurate results significantly faster than the traditional brute-force approach.