The food product is provided with a thermoplastic container (2) and contains a set fermented dairy composition. The body (5) of the container, which defines an interior volume, is provided with a bottom (6) and a side wall (5a) extending along a longitudinal axis (X) from said bottom as far as a top (7). The side wall (5a) has an annular and preferably circular cross-section. The dairy composition is in contact with an interior surface of the bottom (6) and with a projection element that protrudes inside the container. The projection element (22) prevents rotation of the dairy composition. The projection element is arranged to define an irregular annular area between the projection and the side wall (5a). A process of making the food product is also provided.