The martian polar regions have layered deposits of ice and dust. The stratigraphy of these deposits is exposed within scarps and trough walls and is thought to have formed due to climate variations in the past. Insolation has varied significantly over time and caused dramatic changes in climate, but it has remained unclear whether insolation variations could be linked to the stratigraphic record. We present a model of layer formation based on physical processes that expresses polar deposition rates of ice and dust in terms of insolation. In this model, layer formation is controlled by the insolation record, and dust-rich layers form by two mechanisms: (1) increased summer sublimation during high obliquity, and (2) variations in the polar deposition of dust modulated by obliquity variations. The model is simple, yet physically plausible, and allows for investigations of the climate control of the polar layered deposits (PLD). We compare the model to a stratigraphic column obtained from the north polar layered deposits (NPLD) (Fishbaugh, K.E., Hvidberg, C.S., Byrne, S., Russel, P.S., Herkenhoff, K.E., Winstrup, M., Kirk, R. [2010a]. Geophys. Res. Lett., 37, L07201) and show that the model can be tuned to reproduce complex layer sequences. The comparison with observations cannot uniquely constrain the PLD chronology, and it is limited by our interpretation of the observed stratigraphic column as a proxy for NPLD composition. We identified, however, a set of parameters that provides a chronology of the NPLD tied to the insolation record and consistently explains layer formation in accordance with observations of NPLD stratigraphy. This model dates the top 500 m of the NPLD back to ∼1 million years with an average net deposition rate of ice and dust of 0.55 mm a−1. The model stratigraphy contains a quasi-periodic ∼30 m cycle, similar to a previously suggested cycle in brightness profiles from the NPLD (Laskar, J., Levrard, B., Mustard, F. . Nature, 419, 375–377; Milkovich, S., Head, J.W. . J. Geophys. Res. 110), but here related to half of the obliquity cycles of 120 and 99 kyr and resulting from a combination of the two layer formation mechanisms. Further investigations of the non-linear insolation control of PLD formation should consider data from other geographical locations and include radar data and other stratigraphic datasets that can constrain the composition and stratigraphy of the NPLD layers.