  We show that blow up of solutions with arbitrary positive initial energy of
the Cauchy problem for the abstract wacve eqation of the form $Pu_{tt}+Au=F(u)
\ (*)$ in a Hilbert space, where $P,A$ are positive linear operators and
$F(\cdot)$ is a continuously differentiable gradient operator can be obtained
from the result of H.A. Levine on the growth of solutions of the Cauchy problem
for (*). This result is applied to the study of inital boundary value problems
for nonlinear Klein-Gordon equations, generalized Boussinesq equations and
nonlinear plate equations. A result on blow up of solutions with positive
initial energy of the initial boundary value problem for wave equation under
nonlinear boundary condition is also obtained.
