We performed a biomechanical study using 60 Sawbones® rigid foam blocks of two simulated densities (osteoporotic, n = 30 and non-osteoporotic, n = 30) and 10 cadaveric trapezium bones from fresh-frozen, unembalmed adult cadaver hands to assess the trapezial prosthetic cup migration with progressively greater compression loads (10–40 kg). Two cups from the Touch® prosthesis were compared: 9-mm conical cup and 9-mm spherical cup. Uniaxial compression tests were carried out using an MTS Criterion® Series 40 Electromechanical Testing System. Cup migration was measured in millimeters (mm) at 10, 20, and 40 kg of compression load. Median cup migration values were similar in the cadaveric trapezium bones and Sawbones® non-osteoporotic blocks, and higher in the Sawbones® osteoporotic blocks. In the cadaveric trapezium bones and the Sawbones® non-osteoporotic blocks, migration values were less than or equal to 0.1 mm for 10 and 20 kg loads; it was 0.2 mm for 40 kg load. In the Sawbones® osteoporotic blocks, migration values were less than or equal to 0.3 mm for 10 and 20 kg loads; it was 0.4–0.5 mm for 40 kg load. There was no significant difference between the two cup shapes in both cadaveric trapezium bones and Sawbones® non-osteoporotic blocks. In Sawbones® osteoporotic blocks, the largest difference between the two cup shapes was 0.1 mm for loads up to 40 kg, which corresponded to our measurement accuracy. Our findings indicate that the trapezial component of total trapeziometacarpal joint arthroplasty undergoes very weak migration for axial compression loads up to 40 kg, presumably below the threshold of clinical relevance. The cup shape did not have an obvious influence; however, low bone mineral density may result in greater cup migration.