With increasing interest in the use of additive manufacturing techniques in the construction industry, static rheological properties of fresh concrete have necessarily come into focus. In particular, the knowledge and control of static yield stress (SYS) and its development over time are crucial for mastering formwork-free construction, e.g. by means of layered extrusion. Furthermore, solid understanding of the influences of various concrete constituents on the initial SYS of the mixture and the structural build-up rate is required for purposeful material design. This contribution is concentrated on the effect of aggregates on these rheological parameters. The volume fraction of aggregates was varied in the range of 35 to 55 % by volume under condition of constant total surface area of the particles. The total surface area per unit volume of cement paste was equal to 5.00, 7.25 and 10.00 m²/l, conditioned on the constant volume fraction of aggregates. Both variations were enabled by changing the particle size distributions of the aggregates while holding the cement paste composition constant for all concrete mixtures. To characterise the SYS and the structural build-up, constant shear rate tests with a vane-geometry rotational rheometer were performed. It was found that in the ranges under investigation the variation in volume fraction had a more pronounced effect on the static rheological properties of concrete than did the variation in surface area. An accurate mathematical description of the relationship between the initial SYS of concrete and the relative volume fraction of aggregate based on the Chateau-Ovarlez-Trung model was proposed. Challenges in deriving a similar relationship for the structural build-up rate of concrete were highlighted.