An experimental method (TWCS method) was applied to determine the flexural elastic modulus E and some other stress-deformation characteristics of a thin-walled circular cylindrical polymer shell at compression. A methodology of test sample preparation and fixation as well as means of the measurement of the load P and the respective displacement A were developed. Two modes of testing the equipment were used in which the sequences of measuring P — A and A — P were implemented. Repeatability of measurements was evaluated. Optimal geometric parameters of test samples and the range of determinable values of modulus E were defined. A procedure of the calculation of the relationship between the tensile stress а and relative elastic tensile deformation e in the most deformed area of the sample was developed. Applicability of the TWCS method for multiple assessments of changes of deformational characteristics by using a single sample was proved. It was shown that creep, creep recovery, and stress relaxation tests can be performed by the TWCS method.