Machine for grinding plate-shaped elements, particularly tiles and slabs of ceramic material, natural stones, glass or the like, comprising: - at least a base frame; - forward movement means for at least a plate-shaped element having at least a first side to be ground and at least a second side transversal to said first side, said forward movement means being fitted on said base frame and being suitable for moving said plate-shaped element on at least a movement surface along at least a direction of forward movement, wherein: - said forward movement means comprise at least a pair of flexible elements (9a, 9b; 10a, 10b) closed on themselves like a loop, each of which is wrapped at least in part around two operating wheels and can be placed in contact on opposite faces of said lilate-shaped element to drive it along said direction of forward movement; and - said forward movement means comprise at least two of said pairs of flexible elements (9a, 9b; 10a, 10b), of which a first pair (9a, 9b) is fitted on a first support structure and a second pair (10a, 10b) is fitted on a second support structure and is arranged substantially alongside and parallel to said first pair (9a, 9b); and - machining means (20, 21) for machining said first side, which are arranged in proximity of said movement surface and are suitable for intercepting said plate-shaped element in its movement along said direction of forward movement, said machining means (20, 21) comprising at least one of a side grinding wheel and a chamfering wheel; characterised by the fact that: - said support structures (12, 13) are associated with said base frame in a reciprocal moving way, approaching and moving away along a transversal direction substantially at right angles to said direction of forward movement; - said machine comprises square positioning means (32, 33, 34, 35) of said plate-shaped element on said movement surface, which comprise at least a first pusher and at least a second pusher moving alternately along said direction of forward movement and are suitable for pushing said second side to place it in a squared-up position substantially at right angles to said direction of forward movement; and - said first pusher is fitted on said first support structure and said second pusher is fitted on said second support structure, wherein said pushers (32, 33) are mobile with said support structures (12, 13) along said transversal direction allowing changing the reciprocal distance of said pushers (32, 33) according to the size of said plate-shaped element being machined. - at least a base frame; - forward movement means for at least a plate-shaped element having at least a first side to be ground and at least a second side transversal to said first side, said forward movement means being fitted on said base frame and being suitable for moving said plate-shaped element on at least a movement surface along at least a direction of forward movement, wherein: - said forward movement means comprise at least a pair of flexible elements (9a, 9b; 10a, 10b) closed on themselves like a loop, each of which is wrapped at least in part around two operating wheels and can be placed in contact on opposite faces of said lilate-shaped element to drive it along said direction of forward movement; and - said forward movement means comprise at least two of said pairs of flexible elements (9a, 9b; 10a, 10b), of which a first pair (9a, 9b) is fitted on a first support structure and a second pair (10a, 10b) is fitted on a second support structure and is arranged substantially alongside and parallel to said first pair (9a, 9b); and - machining means (20, 21) for machining said first side, which are arranged in proximity of said movement surface and are suitable for intercepting said plate-shaped element in its movement along said direction of forward movement, said machining means (20, 21) comprising at least one of a side grinding wheel and a chamfering wheel; characterised by the fact that: - said support structures (12, 13) are associated with said base frame in a reciprocal moving way, approaching and moving away along a transversal direction substantially at right angles to said direction of forward movement; - said machine comprises square positioning means (32, 33, 34, 35) of said plate-shaped element on said movement surface, which comprise at least a first pusher and at least a second pusher moving alternately along said direction of forward movement and are suitable for pushing said second side to place it in a squared-up position substantially at right angles to said direction of forward movement; and - said first pusher is fitted on said first support structure and said second pusher is fitted on said second support structure, wherein said pushers (32, 33) are mobile with said support structures (12, 13) along said transversal direction allowing changing the reciprocal distance of said pushers (32, 33) according to the size of said plate-shaped element being machined.