Grillage foundations may provide an economical alternative to offshore 'mudmat' foundations for seabed infrastructure, owing to their improved hydrodynamic characteristics, which are important during installation. Grillage foundations consist of a mesh of vertical grilles that penetrate the seabed during loading. Offshore loadings on these types of foundation are likely to consist of vertical (mostly dead weight) loading and horizontal 'in-service' loads. However, to date there is no accepted method of design, as foundation capacity may differ significantly from that of conventional solid shallow foundations. This paper presents an analytical method designed to calculate the variation of vertical bearing capacity with grille penetration in sand. The results show that grillages are able to achieve the same capacity as solid foundations of the same breadth, but this requires significant penetration of the grillage. Consequently, design choices are likely to depend on the amount of settlement the structure can tolerate. Simplified analytical equations have been presented to allow calculation of the load settlement response, and to calculate how much settlement is required to mobilise the flat-plate capacity of a solid mudmat of the same overall breadth. The methodology has been validated by comparing results with those from model tests.