Edge trimming apparatus and method for trimming off wavy edges of strip material, e.g. metal strip, wherein rotary trimming knives for each edge of the strip are movable transversely relative to the advancing strip. The knives are pivotally supported about vertical axis and can have their transverse spacing adjusted, the support blocks preferably being transversely slidable in guides which are mounted on a carriage which itself is transversely movable relative to the advancing strip. Edge sensors are located adjacent edge regions of the strip and signals from the sensors are passed to a device, for example a hydraulic jack, for moving the carriage transversely.