The four-dimensional Minkowski space-time is considered as a three-brane em
bedded in five dimensions, using solutions of five-dimensional supergravity
. These backgrounds have a string theoretical interpretation in terms of D3
-brane distributions. By studying linear fluctuations of the graviton we fi
nd a zero-mode representing the massless graviton in four-dimensional space
-time. The novelty of our models is that the graviton spectrum has a genuin
e mass gap (independent of the position of the world-brane) above the zero-
mode or it is discrete. Hence, an effective four-dimensional theory on a br
ane that includes the massless graviton mode is well defined. The gravitati
onal force between point particles deviates from the Newton law by Yukawa-t
ype corrections, which we compute explicitly. We show that the parameters o
f our solutions can be chosen such that these corrections lie within experi
mental bounds.