Greetings Richard:
As far as I know, as foreigner, you can only bring weapons to practice Sport Hunting when coming as tourist.
Anyway, before entering the weapons to the country, an authorization should be processed at the "Registro Nacional de Armas, del Servicio de Material y Armamento del Ejército":
Main Office
Avenida de las Instrucciones 1925
Tel.: 2354 0326 / 2354 0327
Fax: 2355 4153
E-mail: armassma@ejercito.mil.uy
As national or legal resident, to legally buy or import a weapon, you may first process and obtain the "TÃtulo de Habilitación para la Adquisición y Tenencia de Armas (THATA)"
See law relating to that topic on (in spanish):
Best regards,