Implementing DNA computing circuits using components tethered to a surface offers several advantages over using components that freely diffuse in bulk solution. However, automated computational modeling of tethered circuits is far more challenging than for solution-phase circuits, because molecular geometry must be taken into account when deciding whether two tethered species may interact. Here, we tackle this issue by translating a tethered molecular circuit into a constraint problem that encodes the possible physical configurations of the components, using a simple biophysical model. We use a satisfaction modulo theories solver to determine whether the constraint problem associated with a given structure is satisfiable, which corresponds to whether that structure is physically realizable given the constraints imposed by the tether geometry. We apply this technique to example structures from the literature, and discuss how this approach could be integrated with a reaction enumerator to enable fully automated analysis of tethered molecular computing systems. This paper is a significantly revised and extended version of a conference publication: Lakin and Phillips (in Brijder and Qian (eds) Proceedings of the 23rd International Conference on DNA Computing and Molecular Programming. Lecture Notes in Computer Science, vol 10467, pp 1–16, 2017).