Background/Objectives: In rotator cuff-related shoulder pain (RCRSP) without associated tendon rupture, therapeutic exercise is one of the main treatment strategies; however, the mechanisms through which it exerts its effects remain poorly understood. The aim of this study was to analyze the role of two potential mechanisms of action: increases in muscle strength and changes in the microarchitecture of the supraspinatus muscle. Methods: This prospective study included 39 patients with RCRSP treated with a strengthening exercise program. Muscle strength was assessed using dynamometry, and supraspinatus muscle stiffness was evaluated using shear wave elastography (SWE) at baseline and after 6 months of exercise. These measurements were correlated with clinical and perceived improvement in the patients. Results: Thirty-seven patients completed follow-up. At 6 months, 67.6% of participants reported being much better or fully recovered, 29.7% reported being somewhat better, and only one patient (2.7%) reported worsening. Overall, the increase in muscle strength was small. In participants reporting marked improvement or full recovery, strength gains were slightly greater, but a significant increase in supraspinatus muscle stiffness was observed. In contrast, participants with mild improvement or worsening showed smaller strength gains and no changes in muscle stiffness. Conclusions: Strength gains following strengthening exercises in RCRSP are small and of limited clinical relevance. In contrast, increased supraspinatus muscle stiffness assessed by SWE was observed after the exercise intervention and may reflect exercise-related adaptations; however, its biological meaning should be interpreted with caution.