Rock typing based on mineralogical, hydraulic, or petrophysical similarities is important to reservoir characterization and simulation. In the literature, classifying rocks using single-phase data has been widely studied. Most methods use porosity and permeability measurements to identify rocks with similar characteristic pore sizes. In this study, we invoke concepts from critical-path analysis (CPA) and propose a new rock-typing method on the basis of two-phase flow data, such as water relative permeability krw. We classify rocks based on their similarities in the critical pore radius rc at the same effective water saturation Se. For this purpose, we first convert the $Sw−krw$ plots to $Se−rc$ curves and then apply a curve clustering method to identify similar rocks. To evaluate the proposed approach, we simulated flow in pore networks with many different pore-scale properties. By varying the pore-throat size distribution, contact angle, pore coordination number, pore-shape distribution, and clay content, we generated a wide range of pore networks. Overall, two-phase flow in 240 pore networks were simulated. In addition to synthetic pore networks, pore networks were generated based on properties of Berea, Mt. Simon, and Fontainebleau sandstones. By analyzing the single-phase simulation results, we identified 8 and 15 rock types using the porosity-formation factor and reciprocal formation factor-permeability data, respectively. However, using the two-phase data, we detect 12 rock groups.