By making use of the Laplace transform technique, time-dependent first-flight leakage rates from slabs, spherical shells, and spheres with a uniform source distribution and a delta-shaped pulse have been calculated from their steady-state counterparts found in the available literature. Time-dependent solutions for a quadratic source distribution with a delta pulse have been obtained for a slab and a solid sphere. Using the results for a slab and a solid sphere with a uniform source as a Green’s function, the case of a constant source emitting neutrons over a time interval Δt is considered.