This paper presents several experimental techniques and concepts in the process of measuring mechanical properties of very soft tissue in an ex vivo tensile test. Gravitational body force on very soft tissue causes pre-compression and results in a non-uniform initial deformation. The global digital image correlation technique is used to measure the full-field deformation behavior of liver tissue in uniaxial tension testing. A maximum stretching band is observed in the incremental strain field when a region of tissue passes from compression and enters a state of tension. A new method for estimating the zero-strain state is proposed: the zero strain position is close to, but ahead of the position of the maximum stretching band, or in other words, the tangent of a nominal stress-stretch curve reaches minimum at lambda greater or similar 1. The approach, to identify zero strain by using maximum incremental strain, can be implemented in other types of image-based soft tissue analysis. The experimental results of 10 samples from seven porcine livers are presented and material parameters for the Ogden model fit are obtained. The finite element simulation based on the fitted model confirms the effect of gravity on the deformation of very soft tissue and validates our approach.