Two and three dimensional analytical solutions for the strength of anchor plates buried in a cohesionless soil are derived. Anchor plates that are oriented horizontally, vertically and inclined are considered. The aim of the paper is to present simple and understandable solutions based on geometrically defining the mass of soil mobilised by the movement of an anchor. The weight of this soil mass and the soil friction forces acting on it balance the maximum anchor pull which can thus be determined. Corroboration of the analytical solutions has been obtained by model tests of anchors buried in clean dry sand. The model tests and the experimental results that have been obtained are described in Part 2 of this two-part paper.