Tissue mechanics--stiffness, density and impedance contrast--are broadly informative biomarkers across diseases, yet routine CT, MRI, and B-mode ultrasound rarely quantify them directly. While ultrasound tomography (UT) is intrinsically suited to in-vivo biomechanical assessment by capturing transmitted and reflected wavefields, efficient and accurate full-wave scattering models remain a bottleneck. Here, we introduce a generative neural physics framework that fuses generative models with physics-informed partial differential equation (PDE) solvers to produce rapid, high-fidelity 3D quantitative imaging of tissue mechanics. A compact neural surrogate for full-wave propagation is trained on limited cross-modality data, preserving physical accuracy while enabling efficient inversion. This enables, for the first time, accurate and efficient quantitative volumetric imaging of in vivo human breast and musculoskeletal tissues in under ten minutes, providing spatial maps of tissue mechanical properties not available from conventional reflection-mode or standard UT reconstructions. The resulting images reveal biomechanical features in bone, muscle, fat, and glandular tissues, maintaining structural resolution comparable to 3T MRI while providing substantially greater sensitivity to disease-related tissue mechanics.