The risk of hydroplaning and reduction of skid resistance are two major safety concerns in wet weathering traffic operations on highways and runways. The writers earlier developed an analytical computer model to simulate the phenomenon of hydroplaning. The simulation of wet-pavement skid resistance is analytically a more complex problem to handle than hydroplaning simulation. The present paper adopts a more elaborate theoretical approach and proposes an improved analytical computer model to simulate hydroplaning as well as the reduction of wet-pavement skid resistance as the sliding wheel speed increases. The theoretical formulation and development of a three-dimensional finite-element model based on solid mechanics and fluid dynamics is presented. The computed hydroplaning speeds by the proposed model were analyzed and verified against the well-known experimentally derived NASA hydroplaning-speed equation. The analysis confirmed that the NASA equation is a special case of a general solution, and that it is applicable only to a specific range of tire footprint aspect ratios. An analysis of the decreasing trend of wet-pavement skid resistance with vehicle speed and its validation against measured experimental data will be the subject of another paper.