A time domain approach employing the semiclassical approximation to the quantum mechanical propagator, as applied to Gaussian wavepackets, is used to study the barrier penetration problem. We have observed that qualitative agreement with the exact quantum calculations for the correlation function and the transmission probability can be achieved by considering only classically allowed trajectories. The results slowly tend to the classical step function at the barrier top as a function of the wavepacket center parameter, however. We suggest that a full semiclassical calculation, including nonclassical trajectories with complex energies, would improve the results.