We have studied the occurrence of superconductivity under pressure in the C
aSi2 family of compounds, namely the semimetallic trigonal phase and the al
pha-ThSi2-type tetragonal one. Although only the latter is superconducting
(T-c = 1.56 K) at ambient pressure, starting from the trigonal phase and ap
plying high pressure (>12 GPa) we have found a new superconducting phase wi
th T-c(onset) similar to 14 K, among the highest ever found in silicon base
d materials.