Electromagnetic metamaterial, which is usually treated as a homogeneous medium, can manipulate both the far fields and the near fields. On the other hand, due to its artificially structured nature, near fields of high spatial frequencies invoke the nonlocal response of the medium. Here, we study this nonlocality using a dipolar model. From the model, we can derive the effective medium directly and the complete ͑k , ͒ dispersion is used as the starting point in describing the material. We apply the model on the superlensing effect via a slab of double-negative metamaterial. In a particular case the wavelength is a hundred times of the lattice spacing, subwavelength imaging is sensible only when the lens is thinner than three wavelengths. The resolution can be improved by employing a smaller lattice spacing.