A solid support for the solid-phase synthesis of peptides or proteins in high yield and in high purity, suited both to the synthesis of a single peptide or protein and to the parallel and substantially simultaneous synthesis of a plurality thereof, is based on a cross-linked polyolefin, especially polyethylene, substrate, the cross-linking having been obtained by irradiation with high energy electrons or .gamma. radiation or treatment with organic peroxide such as benzoyl peroxide, to which substrate are grafted polymer chains such as polystyrene chains which are functionalized with a chemical functionality facilitating the formation of an anchoring linkage between the polymer moiety and another chemical species. The solid support is also suited for use in solid-phase biosystems, notably bioassays, such as immunoassays, DNA hybridization assays or PCR amplification. The grafted chains may bear substituents which are such that the polymer-grafted cross-linked polyolefin substrate is swellable by water or aqueous media, in other words, hydrophilic, which makes the solid support particularly well suited for assays of the ELISA type.