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Secondary emission from metal surfaces is well described by the theory of Sternglass. His theory and resulting "universal" curve can be applied for planar uncharged surfaces in an energy range from tens of electronvolts to several kiloelectronvolts. However, space dust is composed of silicates, ice, and graphite, i.e., nonconducting materials. Their surfaces are highly curved, and they are usually charged to nonnegligible potentials. Since previous attempts to describe the size effect on emission properties of the dust succeeded only partly, we have used the original Sternglass approach and developed a computer model of secondary emission from small bodies. The model follows individual trajectories of primary electrons inside the grain and, based on simple assumptions consistent with the Sternglass theory, calculates a probability of escaping of the excited electrons. The model provides measurable quantities (the yield of secondary emission, the charge accumulated in the grain, or the surface potential) but it can illustrate processes which are not accessible by direct measurements. Free parameters of the model depend on the grain material and can be determined by a fit of model results to the experimental data. The paper presents model assumptions and results of calculations for spheres of different diameters and two insulating materials. The theoretical results are compared with the laboratory experiment when the grains with approximately 1, 2, 5, and 10 μm of diameter were charged by an electron beam in a range 300 eV-10 keV. The comparison shows a good agreement of the experiment and theory. Moreover, the reversal of the sign of the grain charge in a certain range of beam energies and grain diameters predicted by the model was confirmed by the experiment.