Abstract Kinds of tubular strings are widely applied to oil exploration & development. In the preceding studies, theses tubular strings are usually taken as homogeneous thin rods without connectors constrained in a straight cylinder or torus. Recent studies have indicated that the effect of connectors on the tubular strings is ignorable. On the basis of the previous studies, the paper provides an analytical model describing the helical buckling behaviors of a rod with connectors constrained in a torus. The new model is solved based on beam-column model and minimum potential energy theory. There are three contact cases between the rod and the torus, namely no contact, point contact and wrap contact. The deflections of the rod and critical conditions between different contact cases are calculated. The results show that the deflections and critical conditions are quite different when the equivalent torus curvature radius changes. The effects of equivalent torus curvature radius, rod buckling and connectors on bending moment and contact force are analyzed. The results show that connector is an important factor which should not be neglected.