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Highlights • The coated asperity contact behaviors are studied for the soft coating cases under frictionless and friction condition. • The effect of the strain hardening exponent of the coating, besides the Young's modulus, yield strength and original thickness on the contact behaviors is explored. • The expressions of the contact area and the coating thickness leading to the maximum weakening effect in the loading process is obtained. • An inflection point of the maximum von Mises stress curve in the coating is found, which is related to the locations of maximum stresses. The expressions of the dimensionless von Mises stress and the interference at the inflection point are acquired. Abstract The contact between a rigid flat and a coated asperity is studied using the finite element method under frictionless and friction condition. The soft coating and hard substrate of the asperity are both considered as the power-law hardening elastic–plastic material, which is commonly used in main bearing of the marine engine. The effect of the material and geometrical properties of the coating, including Young's modulus, yield strength, hardening exponent and original coating thickness, on the contact behaviors is studied under the frictionless condition. The change of the contact area and coating thickness in the loading process is explored, and the expressions of the coating thickness which leads to the maximum weakening effect are obtained. The von Mises stress distribution at yield inception and the maximum stress in the loading process in the coating are researched respectively. Also, the friction effect on the contact parameters was considered by integrating the empirical friction coefficient value into the contact model. This work would be helpful to find the optimal material and geometrical properties for the soft coating on the hard substrate which are power-law hardening elastic–plastic materials. [ABSTRACT FROM AUTHOR]