  We introduce an approximation to calculate the gravitational radiation
produced by the collision of true-vacuum bubbles that is simple enough to allow
the simulation of a phase transition by the collision of hundreds of bubbles.
This ``envelope approximation'' neglects the complicated ``overlap'' regions of
colliding bubbles and follows only the evolution of the bubble walls. The
approximation accurately reproduces previous results for the gravitational
radiation from the collision of two scalar-field vacuum bubbles. Using a bubble
nucleation rate given by $\Gamma = \Gamma_0 e^{\beta t}$, we simulate a phase
transition by colliding 20 to 200 bubbles; the fraction of vacuum energy
released into gravity waves is $E_{\rm GW}/E_{\rm vac} = 0.06(H/\beta)^2$ and
the peak of the spectrum occurs at $\omega_{\rm max}=1.6\beta$ ($H^2=8\pi G\rho
/3$ is the Hubble constant associated with the false-vacuum phase). The
spectrum is very similar to that in the two-bubble case, except that the
efficiency of gravity-wave generation is about five times higher, presumably
due to the fact that a given bubble collides with many others. Finally, we
consider two further ``statistical'' approximations, where the gravitational
radiation is computed as an incoherent sum over individual bubbles weighted by
the distribution of bubble sizes. These approximations provide reasonable
estimates of the gravitational-wave spectrum with far less computation.
