In a method and apparatus for determining the elasticity of a material of an examination object, which is included in a subarea of an acquired image volume, data from the image volume are acquired with a tomographic imaging method in at least two different time phases during a body movement of the examination object. At least two recorded images are registered with one another. A deformation field of the material included in the subarea of the acquired image volume is determined from the images which are registered with one another. The local elasticity of the material of the image volume included in the subarea of the acquired image volume is determined on the basis of the determined deformation field.