This paper presents a novel Hall-effect-based magnetic sensor for handheld measurement of either elasticity or tension in soft tissues. A theoretical model is developed for the mechanical interaction of the sensor with the tissue, and conditions are established under which the separate effects of tension or elasticity can be measured. A model of the magnetic field within the sensor is developed and a technique to estimate the sensor response in the presence of multiple magnets is established. This paper then provides analytical sensor responses and compares them with experimental results obtained on synthetic materials. It is found that the sensor can measure tension values upto 100N with a resolution of 10N in handheld operation and elasticity of upto 0.87 MPa with a resolution of 0.02 MPa. Significant experimental characterization and statistical analysis of sensor repeatability is performed. The viability of this sensor to make tension and elasticity measurements with biological tissues is then demonstrated using turkey tendons and fresh swine tissues.