A sand valley is a conjugate problem of sand heap. A typical geometry of planar valley under constant unit weight lying at the angle of repose is illustrated by two adjacent infinite sand heaps. The rigid body of infinite depth of cohesionless material is considered in two-dimensional quasi-static equilibrium. This study reveals the solutions according to a particular description of stress paths where the principal stress orientation provides additional equation to the two equilibrium equations for analyzing three unknowns of stress variables. Closed-form stress solutions for loose sand valley formed at the angle of repose in the planar two-dimension were derived based on the fixed principal axis hypothesis using the Lamé-Maxwell equations of equilibrium. Paths of principal stresses describe self-weight transfer mechanism under the static equilibrium.