This invention relates to a wall module (3) for constructing a wall for a building, wherein the wall module (3) comprises a plurality of spaced upright pillars (1, 10) which are formed in one part, wherein said pillars (11, 12) comprise a plurality of first connecting means which are disposed at a distance from each other and which have been made integral with the pillar (1, 10) and which are provided to cooperate with corresponding second connecting means (27, 24) on an upper edge of one or more wall panels (21, 22) for connecting the one or more wall panels (21, 22) to the spaced apart pillars (1, 10), the second connecting means being arranged on a side facing the pillar (20) of the one or more wall panels. The invention further relates to a housing containing one or more of such wall modules, and roof profiles for mounting a roof.