The purpose of this study was to investigate the impact of using a wrench under isotonic (constant torque) and isokinetic (constant speed) task modes (TM) at three work surface inclinations (WSI) (0°, 45°, and 90°) on the biomechanical (muscle activity) and kinematic (joint posture) responses of the upper extremity. The muscle activity of seven muscles (trapezius posterior deltoid, anterior deltoid, triceps, biceps, brachioradialis, and flexor digitorium) and posture of four body segments (shoulder adduction/abduction, elbow flexion/extension, forearm supination/pronation and wrist flexion/extension) were obtained using surface electromyography and motion tracking, respectively. WSI showed a statistically significant effect on the muscle activity of the posterior deltoid (p = .038), triceps (p = .016), and biceps (p = .021). The least muscle activity was recorded at the 0° WSI in the isotonic TM. WSI had a significant impact on the supination (p = .017) and pronation (p = .011) of the forearm. The 45° WSI had the least impact on forearm postures. Wrenches are widely used in industries, including automobile service and maintenance, manufacturing, carpentry, and general repair work. Their usage poses risks for the development of musculoskeletal disorders in the upper extremity. In spite of this, knowledge of their physical demands and associated impact on the upper extremity has not been well documented. This study provides empirical evidence on the biomechanical and kinematic responses of selected upper extremity muscles and limb segments and highlights task performance and workstation design factors that elicit undue levels of these responses. The results of this work can provide guidance for ergonomic interventions such as optimized task design and/or improved workstation design when it comes to wrench‐turning tasks.