This article presents design and modeling of a novel high-torque bidirectional curl pneumatic artificial muscle (BCPAM) consisting of two identical inflatable semielliptic cylindrical chambers in parallel and symmetric arrangement. Each chamber is enclosed by a hyperelastic silicone (polymer) bladder encircled by an anisotropic elastic fabric sheath in circumference and fastened by conical fittings at two ends. The sheath is composed of rubber-blended polyester-knitted fabric (RPF) with high uniaxial nonlinear elasticity to allow longitudinal stretch and restrict radial expansion of the bladder, and is partially reinforced by polyvinyl chloride (PVC)-coated polyester-woven fabric (PPF) with high in-plane strength working as a neutral limit layer for bending deformation of the BCPAM.