This paper is the first in a series of papers that present a new prediction model for creep and shrinkage of concrete, called for brevity the BP−KX model. This model represents an update and improvement of the BP model published in this journal in 1978–79. The improvement is possible because further experimental data became available in the literature and at the same time knowledge of physical concepts and mechanisms has improved. This first paper presents a prediction model for the mean (overall) shrinkage strain in cross-sections of long members, which takes into account the influence of environmental humidity, the effective thickness of the member, the effect of cross-section shape, the effect of age at the start of drying, and the effect of temperature. The proposed basic form of the shrinkage formulae is fustified by nonlinear diffusion theory for the movement of moisture through concrete. Extensive comparisons with important test data from the literature, altogether 23 data sets, reveal that the predictions are better than with the previous models. Statistics of prediction are also given. The main error of prediction arises from the estimation of the shrinkage parameters from concrete strength and composition. If limited short-time shrinkage data are available, the predictions can be greatly improved.