The paper presents a general constitutive equation for geomaterials allowing to describe dilatancy and/or compressibility during transient and stationary creep. The constitutive equation also describes the instantaneous response of the geomaterial, work-hardening during transient creep, instantaneous failure and creep failure. The damage produced by dilatancy is used to formulate a criterion for creep failure. Thus ultimate failure may be involved in various ways, depending on the initial and boundary conditions and certainly on the constitutive equation. Typical mining engineering examples are given. First is discussed the creep closure of a deep vertical cylindrical cavern, various possible instantaneous failures, creep failure, and spreading of damage by dilatancy into the rock mass. Second example discusses the instantaneous failure and creep failure around a horizontal tunnel, and the location where damage by dilatancy is more pronounced. The third example presents the case of a rectangular-like shaped cavern.