When thin-walled hollow elastic spheres are compressed between two parallel rigid surfaces, there is an initial flattening of the sphere in the contact regions, followed by a snap-through buckling of the flattened surface. As the compression increases the sphere undergoes further buckling modes as a number of ridges and folds are formed. This elastic buckling deformation is investigated using a finite element analysis (FEA) technique. It is shown that the ratio of displacement at buckling to wall thickness depends weakly not only on Poisson's ratio, ν, but also on the ratio of the geometric wall thickness, h, to sphere radius, R. This approach is validated by comparison with experimental compression results on microspheres of approximately 40 µm in diameter to table tennis balls with a diameter of 40 mm.The analysis shows that a simple axial compression of a thin-walled hollow sphere can be used to measure both the average wall thickness of the sphere, from the deformation at the buckling snap-through, and the modulus from the force at this point. This provides a good technique to fully characterise the geometry and the elastic behaviour of thin-walled spheres of any size.