  We study bounce solutions and associated negative modes in the class of
piecewise linear triangular-shaped potentials that may be viewed as
approximations of smooth potentials. In these simple potentials, the bounce
solution and action can be obtained analytically for a general spacetime
dimension $D$. The eigenequations for the fluctuations around the bounce are
universal and have the form of a Schr\"odinger-like equation with
delta-function potentials. This Schr\"odinger equation is solved exactly for
the negative modes whose number is confirmed to be one. The latter result may
justify the usefulness of such piecewise linear potentials in the study of
false vacuum decay.
