Austenitic stainless steel 304L (AISI304L), of varied thickness, is widely used in the fabrication industry and in many cases, it requires contour machining for achieving intricate profiles. Abrasive water jet machine is a proficient alternative for machining difficult-to-cut, reflective, conductive, and heat-sensitive materials such as austenitic stainless steel with complex geometries. However, due to differences in machining responses for varied material conditions, the abrasive waterjet machine experiences challenges such as kerf geometric inaccuracy and low material removal rate. In this study, an abrasive waterjet machine is employed to perform contour cutting of different profiles to investigate the impacts of traverse speed and material thickness in achieving a lower kerf taper angle and higher material removal rate. Experimental results show that all profiles encountered a similar trend of obtaining higher kerf taper angle and material removal rate as traverse speed increased. Analysis of variance revealed that material thickness denotes a more significant impact to kerf taper angle and material removal rate with a contribution within the range of 69%-91% and 62-69% respectively; whereas traverse speed indicates the least contributing factor within the range of 5%-18% in kerf taper angle and 27%-36% for material removal rate.