The ability to render realistic texture perception using haptic devices has been consistently challenging. A key component of texture perception is roughness. When we touch surfaces, mechanoreceptors present under the skin are activated and the information is processed by the nervous system, enabling perception of roughness/smoothness. Several distributed haptic devices capable of producing localized skin stretch have been developed with the aim of rendering realistic roughness perception; however, current state-of-the-art devices rely on device fabrication and psychophysical experimentation to determine whether a device configuration will perform as desired. Predictive models can elucidate physical mechanisms, providing insight and a more effective design iteration process. Since existing models (1, 2) are derived from responses to normal stimuli only, they cannot predict the performance of laterally actuated devices which rely on frictional shear forces to produce localized skin stretch. They are also unable to predict the augmentation of roughness perception when the actuators are spatially dispersed across the contact patch or actuated with a relative phase difference (3). In this study, we have developed a model that can predict the perceived roughness for arbitrary external stimuli and validated it against psychophysical experimental results from different haptic devices reported in literature. The model elucidates two key mechanisms: 1) The variation in the change of strain across the contact patch can predict roughness perception with strong correlation 2) The inclusion of lateral shear forces is essential to correctly predict roughness perception. Using the model can accelerate device optimization by obviating the reliance on trial-and-error approaches.