This paper is concerned with determining the elastic properties of a composite material composed of hollow spherical inclusions embedded in a matrix. Both inclusions and surrounding material are taken to be isotropic and elastic.As the result of a straightforward extension of Hashin's work, upper and lower bounds have been developed for the gross shear modulus of the composite. In addition, a closed form expression is presented for the gross bulk modulus of the material. Numerical results have been presented illustrating the effect of wall thickness of the inclusion upon the elastic constants of the composite. As illustrated by example, control of the properties and geometry of the inclusions permits "design" of a material with prescribed elastic behavior.