Powder-bed beam-based metal additive manufacturing (AM) such as electron beam additive manufacturing (EBAM) and selective laser melting (SLM) has a potential to offer innovative solutions to many challenges faced in the manufacturing industry. However, due to complex heat transport and thermomechanical interactions, the physical process of powder-bed AM has not been fully understood. This dissertation research focuses on the process thermal analysis, thermomechanical modeling and deformation studies of powder-bed metal AM parts. The primary objectives of this research are: (1) to develop a 3D finite element (FE) thermal model to study the powder porosity effect in EBAM, validated by near infrared thermography; (2) to apply the developed thermal model and study, supported by experiments, the thermal response under different process parameters; (3) to simulate the SLM process using the developed 3D thermal model; (4) to develop a 3D thermomechanical FE model to study temperature, stress and deformation characteristics in EBAM overhang parts for different powder sintering conditions; (5) to investigate different support structures for overhang deformation in EBAM; (6) to investigate an overhang support design method for structure optimization. The major findings are summarized as follows. (1) For beam process parameters of 632 mm/s speed, 6.7 mA current and 0.55 mm diameter, the peak temperature is ~2700 °C and melt pool size is 2.94 × 1.09 × 0.12 mm (length, width and depth). (2) Process parameters affect thermal characteristics. For 482 vs. 1595 mm/s speed, given 7.7 mA current and 0.65 mm diameter, the peak temperatures are 2572 vs. 2326 °C and the melt pool lengths are 2.35 vs. 1.25 mm. (3) In SLM, the residual heat can increase the melt pool size from raster scanning; e.g., the melt pool depth changes from ~0.085 mm to ~0.11 mm at given parameters. (4) In thermomechanical simulations, the results revealed that decreasing the powder-bed porosity (50% vs. 35%) can reduce the process temperatures, part residual stresses and overhang deformations. (5) A contact-free heat support beneath an overhang may effectively minimize overhang deformations. (6) The proposed support design methodology may eliminate part overhang deformations using less support materials.