Radioactive particles escaping a surface carry a portion of the disintegration energy. The fluxes of particles, power, and energy are referred to as residual fluxes. In this paper a method is formulated for predicting residual fluxes emanating from a composite surface consisting of an active substrate layer protected by a clad layer. Application of this method requires only knowledge of the particle ranges in the layer materials. Using existing range-energy equations, generalized plots are presented for estimating residual quantities for heavy particles. Calculations show that fractional residual power and particle fluxes vary from 0.5 for thin (monoatomic) layers to zero for very thick layer or heavily cladded systems. Typical values of the residual power are 0.1 W/cm2 for alpha particles and 10 W/cm2 for fissioning surfaces.