Pulsed neutron capture (PNC) logs are commonly used for formation evaluation behind casing and to assess time-lapse variations of hydrocarbon pore volume. Because conventional interpretation methods for Σ logs assume homogeneous formations, errors may arise, especially in thinly bedded formations, when appraising petrophysical properties of hydrocarbon-bearing beds. There exist no quantitative interpretation methods to account for shoulder-bed effects on Σ logs acquired in sand-shale laminated reservoirs. Because of diffusion effects between dissimilar beds, Σ logs acquired in such formations do not obey mixing laws between the Σ responses of pure-sand and pure-shale end members of the sedimentary sequence. We have developed a new numerical method to simulate PNC rapidly and accurately logs. The method makes use of late-time, thermal-neutron flux sensitivity functions (FSFs) to describe the contribution of multilayer formations toward the measured capture cross section. It includes a correction procedure based on 1D neutron diffusion theory that adapts the transport-equation-derived, base-case FSF of a homogeneous formation to simulate the response of vertically heterogeneous formations. Benchmarking exercises indicate that our simulation method yields average differences smaller than two capture units within seconds of computer central processing unit time with respect to PNC logs simulated with rigorous Monte Carlo methods for a wide range of geometrical, petrophysical, and fluid properties.