A delayed coking unit with a coking drum having an upper cylindrical portion and a lower frusto-conical portion is supported by means of a support structure surrounding the cone frustum of the lower portion of the drum; the support structure comprises a cone support member having a concave frusto-conical support surface mating with the outer convex cone frustum of the lower portion of the drum so that the drum sits in the cone support element. The support structure further has a weight supporting member or members attached to the cone support member intermediate its upper and lower peripheries which acts or act to transfer the weight of the drum (and contents) downwards to a suitable sub-structure such as a concrete slab. In a preferred embodiment, the drum may also be stayed against lateral forces by means of guide members at the upper portion of the drum.