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Electric‐field‐induced switching between equilibrium configurations in certain bistable liquid‐crystal geometries is governed by the motion of disclinations, propelled by elastic distortions of the equilibrium states subjected to applied fields. In this paper and the next (paper II), we describe the distortions and energies of bistable planar horizontal and vertical states, and nonplanar twist states in a tilted geometry, using exact numerical solutions of the equilibrium equations as well as a ’’boundary‐layer’’ approximation in the high‐field limit. The calculations illustrate the manner in which the distortions become concentrated in boundary layers within a coherence length from the surface, and show the convergence of the planar and nonplanar vertical states at relatively low fields. Implications for the switching mechanism are discussed. In paper II, the boundary‐layer model is used to describe the forces governing the movement of disclinations in bistable switching, producing a quantitative description of their velocity and justification for a mobility‐limited switching time.