The meniscus provides crucial knee function and damage to it leads to osteoarthritis of the articular cartilage. Accurate measurement of its mechanical properties is therefore important, but there is uncertainty about how the test procedure affects the results, and some key mechanical properties are reported using ad hoc criteria (modulus) or not reported at all (yield). This study quantifies the meniscus' stress–strain curve in circumferential and radial uniaxial tension. A fiber recruitment model was used to represent the toe region of the stress–strain curve, and new reproducible and objective procedures were implemented for identifying the yield point and measuring the elastic modulus. Patterns of strain heterogeneity were identified using strain field measurements. To resolve uncertainty regarding whether rupture location (i.e., midsubstance rupture versus at-grip rupture) influences the measured mechanical properties, types of rupture were classified in detail and compared. Dogbone (DB)-shaped specimens are often used to promote midsubstance rupture; to determine if this is effective, we compared DB and rectangle (R) specimens in both the radial and circumferential directions. In circumferential testing, we also compared expanded tab (ET) specimens under the hypothesis that this shape would more effectively secure the meniscus' curved fibers and thus produce a stiffer response. The fiber recruitment model produced excellent fits to the data. Full fiber recruitment occurred approximately at the yield point, strongly supporting the model's physical interpretation. The strain fields, especially shear and transverse strain, were extremely heterogeneous. The shear strain field was arranged in pronounced bands of alternating positive and negative strain in a pattern similar to the fascicle structure. The site and extent of failure showed great variation, but did not affect the measured mechanical properties. In circumferential tension, ET specimens underwent earlier and more rapid fiber recruitment, had less stretch at yield, and had greater elastic modulus and peak stress. No significant differences were observed between R and DB specimens in either circumferential or radial tension. Based on these results, ET specimens are recommended for circumferential tests and R specimens for radial tests. In addition to the data obtained, the procedural and modeling advances made in this study are a significant step forward for meniscus research and are applicable to other fibrous soft tissues.