A sifting machine has a strainer box defining feed-in and discharge points and a free sieve netting surface arranged and tensioned in the strainer box so that a material flow-path is defined across it from the feed-in point to the discharge point. A plurality of striker assemblies may also be arranged in the strainer box for exciting the netting surface. A plurality of fastening and tensioning devices such as clamps are provided along the edges of the netting which are parallel to the direction of the material flow-path for individually tensioning the netting, in a direction transverse to the flow-path, at different points spaced in the direction of the flow-path such that the netting is transversely tensioned to different tensions along the direction of the flow-path. Similar devices may be provided along at least one edge of the netting parallel to the material flow-path for individually tensioning the netting, in the direction of the flow-path, at different points spaced transversely to the direction of the flow-path. The striker assemblies may be operated synchronously or asynchronously.