A finite elastostatic analysis of the singular equilibrium field in the proximity of the apex of a wedge, with clamped-free radial edges and general far-field loading conditions, is performed. The problem is formulated for compressible hyperelastic sheets under a plane stress condition. An asymptotic procedure is proposed to compute the deformation and stress singular fields. Emphasis is placed on the investigation of the dependence of the order of singularity in the asymptotic Piola-Kirchhoff and Cauchy stresses on the wedge angles. The case of a half-plane bounded to a rigid substrate is studied in detail.