AbstractHuman fresh‐frozen cadaveric glenoid labrae from 16 donors were harvested and ten of these had no gross degeneration. These ten were divided into eight equal circumferential sections. Each section was cut to produce test‐samples from the core layer with a cross‐section of 1 × 1 mm. Tensile testing was performed within a controlled environment unit at 37 ± 1 °C and 100% relative humidity. Each test‐sample was precycled to a quasi‐static state to alleviate the effects of deep‐freezing, prior to final testing. The tangent modulus was calculated for each test‐sample before and after a 5‐min period of stress relaxation and at yield. The mean elastic modulus and yield stress of the glenoid labrum were 22.8 ± 11.4 and 2.5 ± 2.1 MPa, respectively. The anterosuperior portion had a lower elastic modulus and lower yield stress than the inferior portion (both P < 0.02). The pre‐stress relaxation tangent modulus was significantly lower than the post‐stress relaxation tangent modulus for all portions of the labrum. The glenoid labrum has similar tensile material properties to articular cartilage. Its elastic modulus varies around its circumference. This suggests that the labrum may encounter different forces at different positions.