In quasi-static tension and compression tests of thermoplastics, full-field strain distribution on the gage section of the specimen can be captured using the two-dimensional digital image correlation method. By loading the test specimens made of a talc-filled and impact-modified polypropylene up to tensile failure and large compressive strains, this study has revealed that inhomogeneous deformation within the gage section occurs quite early for both test types. This leads to the challenge of characterizing the mechanical properties - some mechanical properties such as stress-strain relationship and fracture strain could depend on the measured section length and location. To study this problem, the true stress versus true strain curves determined locally in different regions within the gage length are compared. The results show that, for the tension test, the stress-strain curve seems independent of regions within the gage section, but the local fracture strain increases as the length of the measurement region is reduced. For the compression test, the large transverse expansion of the material in the middle of the gage section causes the specimen surface to become shorter and bulged out in the late stage of the tests, which makes the test result only reliable when the longitudinal strain is smaller than 0.2. A possible inverse-engineering method is proposed for identifying the true material response at a large compressive deformation. It is also shown that the ratio of longitudinal strain to transverse strain is different between tension and compression tests. This difference is not addressed in any existing material models in the finite element software LS-DYNA.