The application of standard techniques of noise estimation to complex machinery has confronted us with several practical problems. Our solutions to some of these problems for internal-combustion engines and transmissions are reviewed here. Designed to estimate the sound radiated from a proposed machine, the methods center on the synthesis of finite-element (FEM) models and test data of related machinery with a finite-element prediction of the conceptual machine. For example, engines similar to a conceptual engine are experimentally characterized in terms of surface vibration velocities and radiation efficiencies over the surface of an engine, with frequency, type, and location of structural excitation as parameters. Finite element models of these engines supplement the data as necessary, leading to a radiation model of the engines which must be analytically modified to apply to the conceptual engine. Then, a detailed FEM model of the conceptual engine predicts transfer functions between structural excitation (combustion, rotation of internals, etc.) and surface velocities. These functions, together with the radiation model, can predict the noise emission from the new engine. Some difficult practical issues are the prediction of differences in forcing functions and vibration transfer functions between existing and proposed machinery, the characterization of combustion noise, and the simplification of models for surface vibration and radiation efficiency. These issues arise in part from a desire to reduce the time and expense of numerical computations.