A method to calculate residual activation of accelerator components is presented. A model for residual dose estimation for thick objects made of arbitrary composite materials for arbitrary irradiation and cooling times is employed in the study. A scaling procedure for applying the model to thin objects with linear dimensions less than a fraction of a nuclear interaction length is described. The scaling has been performed for various materials, and corresponding factors have been determined for objects of certain shapes (slab, solid, and hollow cylinder) that can serve as models for beam pipes, magnets, and collimators. Both contact residual dose and dose attenuation in the air outside irradiated objects are considered. A relation between continuous and pulsed irradiation is accounted for as well.