We study numerically the influence of confinement on the solid fraction and on the structure of three-dimensional random close-packed granular materials subject to gravity. The effects of grain shape (spherical or polyhedral), material polydispersity, and confining wall friction on this dependence are investigated. In agreement with a simple geometrical model, the solid fraction is found to decrease linearly for increasing confinement no matter the grain shape. Furthermore, this decrease remains valid for bidisperse sphere packings, although the gradient seems to reduce significantly when the proportion of small particles reaches 40% by volume. The confinement effect on the coordination number is also captured by an extension of the aforementioned model.