This paper presents a simple method for obtaining the elastic modulus and Poisson’s ratio by using a thin tube subjected to a uniform pressure. The primary target of the present work is a nuclear fuel tube, whose mechanical properties are enhanced by adding a strengthening material into the base material of zirconium alloy, e.g., a coating or a composite. It is particularly useful if the mechanical properties of the strengthening material are not provided because the conventional models of micromechanics or composite materials need the properties of all constituent materials to evaluate its effective mechanical properties. A typical example is an oxide dispersion strengthened (ODS) coated tube for an accident tolerant fuel (ATF), which is currently being developed in the worldwide nuclear field after the Fukushima accident in 2011. In this work, fuel tube specimens of pure Zircaloy-4 and those coated with the ODS are used for the experiments. A pressure of 12.76–38.29 (max) MPa is exerted inside the tubes. The elastic modulus and Poisson’s ratio of the tube material are obtained using Hooke’s law of plane stress condition and the measured axial and circumferential strains. As a result, the elastic modulus and Poisson’s ratio of the pure Zircaloy-4 are very close to the values in the open database, which validates the present method. The difference of the elastic modulus and Poisson’s ratio are not meaningfully appear for the ODS coated tube compared with those of the pure Zircaloy-4 tube. Possible experimental errors and the thin tube assumption are discussed with a simple finite element analysis.