This paper presents a model for the elasticity of semiflexible biopolymer networks, such as F-actin, which are crucial components of the cell cytoskeleton. The model explains the elastic properties of these networks, including the concentration dependence of the storage modulus and yield strain. Unlike classical rubber elasticity, the elasticity of these networks arises from nonclassical rubber elasticity due to the semiflexible nature of the filaments. The persistence length of the filaments is comparable to or larger than the characteristic mesh size of the network, which is a key factor in determining the elastic behavior. The model considers the behavior of semiflexible chains in entangled solutions and densely crosslinked gels. The elastic properties of these networks are influenced by the entanglement length and the mesh size. The model predicts that the plateau modulus scales with concentration as $ G' \sim c_{A}^{11/5} $ for entangled solutions and $ G' \sim c_{A}^{5/2} $ for densely crosslinked gels. The model also explains the observed strain hardening of actin networks and the dependence of the yield strain on the flexibility of the network. The model is based on the energy of semiflexible chains under shear deformation, considering both the bending of the chain and the work done against applied tension. The results are consistent with experimental observations of the shear modulus and yield strain for varying actin concentrations and changes in F-actin stiffness. The model provides a framework for understanding the viscoelastic behavior of biopolymer gels and solutions, and it can explain the large storage moduli and strain hardening observed in semiflexible networks. The model also predicts that the viscoelasticity of dilute filament networks is highly sensitive to filament length, especially for stiff polymers. This sensitivity is due to the entanglement length required for effects on elasticity being much greater than the mesh size, which depends on the bending modulus. The model has implications for the regulation of cytoskeletal actin filaments in cells, as their length is tightly controlled by proteins.This paper presents a model for the elasticity of semiflexible biopolymer networks, such as F-actin, which are crucial components of the cell cytoskeleton. The model explains the elastic properties of these networks, including the concentration dependence of the storage modulus and yield strain. Unlike classical rubber elasticity, the elasticity of these networks arises from nonclassical rubber elasticity due to the semiflexible nature of the filaments. The persistence length of the filaments is comparable to or larger than the characteristic mesh size of the network, which is a key factor in determining the elastic behavior. The model considers the behavior of semiflexible chains in entangled solutions and densely crosslinked gels. The elastic properties of these networks are influenced by the entanglement length and the mesh size. The model predicts that the plateau modulus scales with concentration as $ G' \sim c_{A}^{11/5} $ for entangled solutions and $ G' \sim c_{A}^{5/2} $ for densely crosslinked gels. The model also explains the observed strain hardening of actin networks and the dependence of the yield strain on the flexibility of the network. The model is based on the energy of semiflexible chains under shear deformation, considering both the bending of the chain and the work done against applied tension. The results are consistent with experimental observations of the shear modulus and yield strain for varying actin concentrations and changes in F-actin stiffness. The model provides a framework for understanding the viscoelastic behavior of biopolymer gels and solutions, and it can explain the large storage moduli and strain hardening observed in semiflexible networks. The model also predicts that the viscoelasticity of dilute filament networks is highly sensitive to filament length, especially for stiff polymers. This sensitivity is due to the entanglement length required for effects on elasticity being much greater than the mesh size, which depends on the bending modulus. The model has implications for the regulation of cytoskeletal actin filaments in cells, as their length is tightly controlled by proteins.