Process for the preparation of a fibrous product comprising protein, which process comprises the steps of (a) preparing a homogenous mixture of protein material comprising milk protein material, a hydrocolloid which precipitates with metal cations, and water in the presence of a calcium complex-forming agent at a temperature between 50 °C and 90 °C; (b) adding a solution of a metal cation with a valency of at least 2 to the mixture obtained in step (a) in order to form the fibrous product; (c) isolating the fibrous product; (d) cooling the fibrous product, wherein in step (d) the fibrous product is cooled to a temperature below 10 °C, preferably between 0 and 7 °C, by vacuum cooling. The product thus obtained is particularly suitable for use in preparing meat substitute products.