The pressure melting processes of a block of ice around a moving, horizontal, elliptical cylinder are investigated. The film thickness of liquid and the relation between the force exerted on the elliptical cylinder and the melting velocity are obtained analytically. The results include those of pressure melting around a horizontal cylinder, and are discussed and compared with that of ΔT-driven melting around an elliptical cylinder. The basic differences between Δp-driven and ΔT-driven melting are obtained. Some important conclusions are drawn.