The conventional model of compression test, cylindrical profile model (CPM), ignores shearing deformation in the sample and yields an unrealistic solution. This article presents a new kinematic model and a closed-form solution for barrelled compression test. This model, exponential profile model (EPM), accounts for shear deformation in the test sample and provides a foundation to develop a detailed constitutive framework. To benchmark EPM, example solutions of the test are performed using a finite element model. The example results are compared with those of CPM. It is shown that CPM cannot evaluate the test's real and non-uniform deformation. It is also shown that EPM's predictions comply reasonably well with the finite element results. The importance of the presented solution can be better understood by noting that closed-form solutions of the mechanical tests are the most convenient routes to post process the raw test data and eventually to characterize the sample's material. It is concluded that EPM is a far more reliable platform compared to CPM for meaningful interpretations of the test results.