The purpose of this article is to develop a mathematical model that describes photocure and photopolymerization kinetics. This model is neither wholly phenomenological nor mechanistic, but contains elements of both. We draw an analogy between the classical Avrami approach for first-order phase transformations and the kinetic phenomena that occur during photocuring, and take into account cure inhibition due to a decrease in mobility of the constituents. The result is an explicit algebraic two-parameter expression for the extent of cure versus time. More importantly, the two parameters have physical significance, and to some extent can be predicted a priori. The model is compared to three sets of unrelated data, and excellent agreement is obtained, except for part of the data at the onset of the reactions. Physical insight obtained by comparing our theory with experiments supports the existence of preferred sites for initiating the reaction, and indicates that irradiation is the rate-limiting step in the overall cure process in the limit of small irradiation intensities.