Substrate-assisted self-assembly [S. Hamada and S. Murata, Angew. Chem., Int. Ed., 2009, 48, 6820; X. Sun et al., J. Am. Chem. Soc., 2009, 131, 13248] is a novel methodology for DNA self-assembly to fabricate large-scale DNA nanostructures on substrate surfaces. Although a qualitative explanation of this phenomenon and some experimental results exist, the mechanism is not yet thoroughly understood. A theoretical framework will improve understanding and enable us to exploit this phenomenon for further development and future applications. Here, we propose a model and simulations describing this phenomenon, with comparison to experimental results. The model is based on simple thermodynamics and was converted into quasi-static kinetics to trace the overall process of adsorption and self-assembly during annealing. As an example, a simulation of T-motif Ring formation based on this model successfully reproduced the difference between yields in solution and on a surface, consistent with experimental observations.