The characteristics of anisotropic material, finite deformation, and lubrication in biological system diminish the friction and wear between soft tissues with relative motion. In this research, the lubrication between pleura surfaces in relative motion is analyzed by soft elastohydrodynamic lubrication (soft-EHL) line contact with an equivalent model. The model is a soft, transversely isotropic (TI) elastic strip with finite thickness sliding under a rigid sinusoidal surface, which is used to simulate the surface irregularities, with lubricant in between. The material nonlinearity and the curvature effects due to finite deformation, which are significant in soft-EHL, are considered in the present study. The pressure distribution, film thickness, von Mises stress, and material deformation are analyzed and discussed under various combinations of elastic moduli and Poisson's ratios for the transversely isotropic models. The simulation results reveal that the soft-EHL modeling fit actual result better than the traditional EHL (t-EHL) modeling. The Poisson's ratio νp = 0.1 and νpz = 0.49 situation will have more gentle stress distribution. The present soft-EHL solver can be used to realize some desired stress distributions and to identify the mechanical properties bio-materials under the aids of experiments.