A mathematical model of waste dissolution that includes the formation of secondary solid precipitate(s) explicitly is formulated. For a static type of experiment, the model indicates that the concentration of the highly soluble species compared to the concentration of the main component of the matrix is equal to their corresponding density in the matrix (i.e., congruent release). For low solubility nuclides, the solubility limit of precipitate(s) may be exceeded (depending on the waste composition) and a supersaturated solution is temporarily achieved. From the model, the concentration of radionuclides and mass flux at the waste form surface in a geologic repository is obtained. Numerical results (Sr-90) indicate that the liquid-surface concentration rises very rapidly after dissolution starts. In the first week, the solubility limit of Sr precipitate(s) is exceeded and Sr solid precipitate(s) will be formed. Subsequently the concentration decreases and becomes almost equal to the solubility limit and remains so for up to 1 year. It decreases later due to radioactive decay. After the first week, the surface concentration and surface mass flux are independent of the retardation coefficient throughout the leaching process. The mass transfer rate is determined by the matrix dissolution rate and not by the solubility of the precipitate.