We present a comprehensive neural network to model the deformation of human soft tissues including muscle, tendon, fat and skin. Our approach provides kinematic and active correctives to linear blend skinning that enhance the realism of soft tissue deformation at modest computational cost, aiming to revolutionize character animation in the context of metaverse and game development. Our network accounts for deformations induced by changes in the underlying skeletal joint state as well as the active contractile state of relevant muscles. Training is done to approximate quasistatic equilibria produced from physics-based simulation of hyperelastic soft tissues in close contact. We use a layered approach to equilibrium data generation where deformation of muscle is computed first, followed by an inner skin/fascia layer, and lastly a fat layer between the fascia and outer skin. We show that a simple network model which decouples the dependence on skeletal kinematics and muscle activation state can produce compelling behaviors with modest training data burden. Active contraction of muscles is estimated using inverse dynamics where muscle moment arms are accurately predicted using the neural network to model kinematic musculotendon geometry. Results demonstrate the ability to accurately replicate compelling musculoskeletal and skin deformation behaviors over a representative range of motions, including the effects of added weights.Additionally, we present significant advancements in several related areas of the pipeline including a dynamic mode capture paradigm for augmenting secondary effects on top of our network, a robust meshing algorithm for generating volumetric hexahedron meshes from self-intersecting surfaces and a novel position-based nonlinear Gauss-Seidel approach for quasistatic simulation.