Pressure dependences of longitudinal sound velocities, in the two phases Si-I and Si-V of silicon having, respectively, cubic-diamond and primitive-hexagonal structures, are measured using the technique of picosecond laser ultrasonics adapted to samples compressed in a diamond anvil cell (DAC). For the Si-I phase, stable at atmospheric pressure, the longitudinal sound velocity along the h100i direction is obtained in a single crystal up to 9 GPa. In the case of the Si-V phase, the average sound velocity for an isotropic polycrystalline sample VL(avg) is measured for the first time between 18 and 27 GPa. Above this pressure, preferred orientation of the hexagonal crystallites of Si-V, with their c-axes parallel to the compressional direction in the DAC and to the acoustic pulse propagation direction, is progressively developing thus precluding further VL(avg) measurement. The experimental single crystal elastic constants C11(P) and C12(P) of Si-I, and the shear modulus of polycrystalline Si-V deduced here are in a very good agreement with our first principles calculations and with the earlier results reported for Si-I.