This paper presents a new model of the drilling response of roller-cone bits. First, a set of relations between the weight-on-bit $W$, the torque-on-bit $T$, the rate of penetration $V$, and the angular velocity $\Omega $ is established in the spirit of the model developed for polycrystalline diamond compact (PDC) bits. In contrast to models that depend on a precise description of the bit, the drilling response is investigated by lumping the effect of the bit geometry into a few parameters and on averaging the drilling quantities $(W,T,V,\Omega )$ over at least one revolution of the bit. Within the framework of the model, quantitative information from drilling data related to rock properties, bit conditions, and drilling efficiency can be extracted. Finally, a series of laboratory tests at atmospheric pressure conducted with an in-house designed drilling rig, together with published experimental data, is used to evaluate the proposed model. The good match between the experimental results and the theoretical predictions are promising in regard to the potential use of this model to investigate the drilling response of roller-cone bits.