Bucket foundations are considered to be environmentally friendly foundations. Their stiffness determines the resonant frequencies and fatigue life of the supported offshore wind turbines. This study proposes a rigorous three-dimensional (3D) elastic solution for the stiffness of laterally loaded bucket foundations in different soil profiles. The lumped spring stiffness acting on the top of the bucket and the exact distribution of the distributed soil spring stiffness along the bucket are first obtained from the analytical model. Closed-form formulae for the lumped spring stiffness are then fitted and verified with the existing studies. To facilitate the engineering application, the distributed soil spring stiffness is then averaged to a uniform distribution using the equivalent work method. Two types of simplified Winkler models are finally proposed and calibrated: one in which the spring stiffness is uniformly distributed along the bucket, and the other in which the distributed Winkler springs are divided into two parts bounded by the centre of rotation. The non-dimensional Winkler springs are mainly related to the bucket aspect ratio, the soil Poisson's ratio and the loading height. It is shown that the lateral soil springs alone, asp-y springs for piles, are not sufficient for bucket foundations. The combined two-part p-y springs and uniform rotational springs are suggested to obtain accurate bucket foundation responses.