The main goal of this contribution is to provide a simple method for constructing transversely isotropic polyconvex functions suitable for the description of biological soft tissues. The advantage of our approach is that only a few parameters are necessary to approximate a variety of stress–strain curves and to satisfy the condition of a stress-free reference configuration a priori in the framework of polyconvexity. The proposed polyconvex stored energies are embedded into the concept of structural tensors and the representation theorems for isotropic tensor functions are utilized. As an example, the medial layer of a human abdominal aorta is investigated, modeled by some of the proposed polyconvex functions and compared with experimental data. Hereby, the economic fitting to experimental data, and hence the easy handling of the functions is shown.