In this study, we attempted to model the cuttings lag‐depth distribution caused by the dispersion of cuttings transport velocity in directional drilling. From the results of cuttings lag experiments, it was found that the lag distribution could be modeled using the lognormal distribution probability density function (PDF). A simple formulation of lag‐depth distribution for the entire depth of a well was mathematically derived. Simulation studies of lag depth for a realistic model of a directional well based on field data were conducted to evaluate depth resolution of mud logging. The key finding is that cuttings sampled at the surface can be contaminated by cuttings originating from other unintended depths to the extent of being non‐negligible. This tendency of obscuring the formations and depths from which the sampled cuttings originate is significant if the high inclination or horizontal hole section exceeds a certain length depending on the rate of penetration (ROP). The presented approach has the ability to quantitatively evaluate the uncertainty in the depth resolution of mud logging; this is crucial in improving the lateral quality of reservoir characterization.