Professor Williams obtained a PhD in laser physics at London University and subsequently spent five years at Edinburgh Instruments, a small company producing lasers and laser systems. In this time, he was involved in developing accessories for CO2 waveguide lasers and producing industrial and medical laser systems. In 1987 Stewart moved to the Advanced Technology Centre of BAE Systems where he managed a group whose main area of research was laser processing of aerospace materials. This research included welding, cutting, drilling, micromachining, and surface treatment of a wide range of materials such as aluminium, titanium and carbon fibre reinforced composites.

In 2006 Stewart moved to Cranfield University to take a chair in Welding Science and Engineering and become Director of the Welding Engineering and Laser Processing Centre (WELP). Here he continues to apply his experience and knowledge of material processing in a wide range of research areas but with a particular focus on additive manufacture and laser processing. Since 2013, Stewart successfully delivered projects of more than £30M, including: 2 x EPSRC (CIM in Laser-Based Production 14-19, HiDepAM 2013-16), 4 x Innovate (OAAM 18-21, RoboWAAM 17-21, RAWFEED 13-17, WAAM for Propellant tanks 15-16), 3 x EU (AMAZE 12-17, LASIMM 16–19, ADMIRE 17-20), ~30 individual industrial contracts and many PhD and MSc projects. SW won the Larke Lillicrap award for impact and innovation in novel welding and joining from TWI in 2017.

Professor Williams is director of the WAAMMat industrial collaboration programme, which has been maturing WAAM technology for 8 years. He is also Technical Director and co-founder of WAAM3D, a company set up to supply WAAM technology to industry.

In his spare time Professor Williams likes walking his dogs, playing golf, meteorology, and cooking.