A method for the solid-phase synthesis of peptides or proteins in high yield and high purity uses a solid support consisting of a functionalized polystyrene-grafted polymer substrate, the grafted polystyrene chains being substantially non-cross-linked and having a chain molecular weight, not including optional non-reactive substituents, of at least 200,000, preferably in the range of 600,000-1,200,000. Particularly suitable polymer substrates are substrates of a polyolefin such as polyethylene. The method is particularly well-suited to the compartmentalized synthesis of a multitude of peptides or proteins in a parallel and substantially simultaneous fashion. Preferred embodiments of a solid support for performing the synthesis are prepared from thin polyethylene sheet or film which has been grafted with polystyrene chains in a radical-initiated process in which the polyethylene sheet or film is immersed in a solution of optionally substituted styrene monomer in an alcohol such as methanol, the volume percentage of styrene in the solution preferably being about 30 % v/v, and subjected to gamma irradiation.