The amorphous aggregation of proteins is associated with many phenomena, ranging from the formation of protein wine haze to the development of cataract in the eye lens and the precipitation of recombinant proteins during their expression and purification. While much literature exists describing models for linear protein aggregation, such as amyloid fibril formation, there are few reports of models which address amorphous aggregation. Here, we propose a model to describe the amorphous aggregation of proteins which is also more widely applicable to other situations where a similar process occurs, such as in the formation of colloids and nanoclusters. As first applications of the model, we have tested it against experimental turbidimetry data of three proteins relevant to the wine industry and biochemistry, namely, thaumatin, a thaumatinlike protein, and alpha-lactalbumin. The model is very robust and describes amorphous experimental data to a high degree of accuracy. Details about the aggregation process, such as shape parameters of the aggregates and rate constants, can also be extracted.