Wear model for predicting the vehaviour of a depth is considered in this paper. It is deduced from the energy and volume based wear models such as the Archard equation and the workrate model. A new parameter of the equivalent depth ($D_e$= wear volume /worn area) is considered for the wear model of a depth prediction. A concenpt of a dissipated shear energy density is accommodated for in the suggested models. It is found that $D_e$ can distinguish the worn area shape. A cubic of $D_e$($D_e^3$) gives a better linear regression with the volume than that of the maximmum depth $D_{max}e$($D_{max}^3$) does. Both $D_{max}$ and $D_e$ are used for the presently suggested depth-based wear model. As a result, a wear depth profile can be simulated by a model using $D_{max}$. Wear resistance from the concern of an overall depth can be identified by the wear coefficient of the model using $D_e$.