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The concurrent collection of surface electromyography (sEMG) and strain signals is important for many applications, such as human–machine interaction, sign language recognition, and clinical evaluation of muscle function. Nevertheless, the conventional sensor systems made of rigid, bulky components cannot provide a reliable, conformal interface for accurate, continuous measurements of the epidermal physiological signals. Herein, a skin‐interfaced, multifunctional epidermal sensor patch with characteristics of mechanical softness, large stretchability, and wearable conformability for multimodal measurements of sEMG signals and associated skin deformations from various muscle activities and joint motions is reported. The sensor patch features two pairs of stretchable sEMG electrodes and two thin, miniaturized strain sensors, which are connected by stretchable filamentary serpentine interconnects in an open‐meshed structure. Experimental and computational studies reveal the design and operation of the sensor patch, which exhibit stable and repetitive performance even under a 30% stretching strain level. Demonstrations of the sensor patch on the wrist for simple sign language recognition and on the lower back for the flexion‐relaxation phenomenon illustrate its potential for the comprehensive assessment of the muscle activities and related motions of muscle joints.