Surface coatings enhance tribological performance and extend service life. However, differences between coating and substrate properties make it challenging to design coatings that meet contact pair requirements. The study investigates the three-dimensional line contact problem of two cylindrical solids with an elastic coating using a semi-analytical method (SAM) and the conjugate gradient method (CGM). The pressure-displacement and pressure-stress influence coefficients (ICs) are obtained through a Frequency response functions (FRFs) using an FFT-based conversion method. Additionally, considering the axial direction is much longer than the contact width, the ICs summation method is introduced in the model to account for the effect of neighboring region pressures on the stress and displacement distributions within the computational domain. The validity and accuracy of the model are verified by comparing its solution with the analytical solution of Hertzian contact. The research further explores the effect of coating stiffness, coating thickness, and surface friction coefficient on the stress field distribution. The results provide theoretical support for optimizing coating designs and improving surface tribological performance, which could be applied in various engineering applications, such as gears and bearings.