Spiral strands exhibit dissipative bending behavior when subjected to external axial force. To the best of the authors’ knowledge, only the uniaxial bending behavior of spiral strands subjected to constant axial force has been studied in the literature so far. Thanks to a recently developed mixed stress–strain driven computational homogenization for spiral strands, this paper is the first to study the biaxial bending behavior of spiral strands subjected to variable tensile force. Based on the observed anisotropic behavior, a rheological constitutive model equivalent to multilayer spiral strands is proposed to predict their behavior under such loading. For an -layer strand, the proposed model consists of several angularly distributed uniaxial spring systems, referred to as a multiaxial spring system, where each uniaxial spring system consists of a spring and slider-springs. In a uniaxial spring system, the spring represents the slip contribution of all wires to the bending stiffness of the strand, while each slider-spring represents the stick contribution of each layer. A major advantage of the proposed scheme is its straightforward parameter identification, requiring only several monotonic uniaxial bendings under constant axial force. The proposed rheological model has been verified against the responses obtained from the mixed stress–strain driven computational homogenization through several numerical examples. These examples consist of complex uniaxial and biaxial load cases with variable tensile force. It has been shown that the proposed scheme not only predicts the response of the strand, but also provides helpful insight into the complex underlying mechanism of spiral strands. Furthermore, the low computational cost of the proposed models makes them perfect candidates for implementation as a constitutive law in a beam model. Using a single beam with the proposed constitutive law, spiral strand simulations can be performed in a few seconds on a laptop instead of a few hours or days on a supercomputer.