In a sieve apparatus, a housing (1) is provided with an inlet section with a feed inlet for material to be sifted and a discharge section including at least one outlet. Means are provided for vibrating the screen mesh. The housing has two substantially vertical side walls (2), and a screen mesh (5) having at least one side edge (51) is supported by a support structure (6, 7) connected to the respective side wall (2). The support structure includes a support element (7) along each side wall and adapted to support the screen mesh (5). Each support element is provided as a support profile (7) having an inclined support surface (73) for the side edge (51) of the screen mesh and constituting a V-shaped structure protruding into the housing, said support surface (73) meeting a lower surface (74) in an apex (75) located at a distance from the side wall (2) inside the housing (1). Specifically, each V-shaped support profile (7) is formed as an integral part of the respective side wall (2).