  First principles electronic structure calculations of A-15 type Nb$_3$X (X =
Al, Ga, In, Ge and Sn) compounds are performed at ambient and high pressures.
Mechanical stability is confirmed in all the compounds both at ambient as well
as under compression from the calculated elastic constants. We have observed
four holes and two electron Fermi surfaces (FS) for all the compounds studied
and FS nesting feature is observed at M and along X - $\Gamma$ in all the
compounds. A continuous change in the FS topology is observed under pressure in
all the compounds which is also reflected in the calculated elastic constants
and density of states under pressure indicating the Electronic topological
transitions (ETT). The ETT observed at around 21.5 GPa, 17.5 GPa in Nb$_3$Al
and Nb$_3$Ga are in good agreement with the anomalies observed by the
experiments.
