A workpiece feed/clamp apparatus that is used in a cutting machine for cutting a cut position (Wa) of a workpiece set at a cut position on a feed direction and that feeds the workpiece in the feed direction and then fixes the workpiece on a base of the cutting machine, the apparatus comprising: a feed vise mechanism that is provided on an upstream side of the cutting position movably in the feed direction and includes a pair of first and second feed vise jaws (21, 23) that face to each other in a width direction perpendicular to the feed direction and clamp the workpiece, a feed vise moving cylinder that moves the first feed vise jaw in the width direction, and a feed vise shifting cylinder that shifts the second feed vise jaw in the width direction, each of the feed vise moving cylinder and the feed vise shifting cylinder being a hydraulic cylinder; and a downstream main vise mechanism that is provided just on a downstream side of the cutting position and includes a pair of first and second downstream main vise jaws (77, 79) that face to each other in the width direction and clamp a portion (Wf) correspondent to a product in the workpiece, a downstream main moving cylinder that moves the first downstream main vise jaw in the width direction, and a downstream main shifting cylinder that shifts the second downstream main vise jaw in the width direction, each of the downstream main moving cylinder and the downstream main shifting cylinder being a hydraulic cylinder, characterized in that the downstream main vise mechanism is configured such that a thrust force of the downstream main shifting cylinder toward one side in the width direction is made equal to a thrust force of the downstream main moving cylinder toward another side in the width direction, wherein a position in the width direction where a vise surface of the second of the feed vise jaws (21, 23) is located when the feed vise shifting cylinder reaches a stroke end on an extended side thereof serves as a vise reference position, and wherein the downstream main vise mechanism is configured to locate, if a leading end portion of the workpiece curves, the vise surface of the second downstream main vise jaw at the one side or the other side of the vise reference position in the width direction according to a curvature of the leading end portion of the workpiece when the portion (Wf) correspondent to the product in the workpiece is clamped by cooperation of the first and second downstream main vise jaws (77, 79). a feed vise mechanism that is provided on an upstream side of the cutting position movably in the feed direction and includes a pair of first and second feed vise jaws (21, 23) that face to each other in a width direction perpendicular to the feed direction and clamp the workpiece, a feed vise moving cylinder that moves the first feed vise jaw in the width direction, and a feed vise shifting cylinder that shifts the second feed vise jaw in the width direction, each of the feed vise moving cylinder and the feed vise shifting cylinder being a hydraulic cylinder; and a downstream main vise mechanism that is provided just on a downstream side of the cutting position and includes a pair of first and second downstream main vise jaws (77, 79) that face to each other in the width direction and clamp a portion (Wf) correspondent to a product in the workpiece, a downstream main moving cylinder that moves the first downstream main vise jaw in the width direction, and a downstream main shifting cylinder that shifts the second downstream main vise jaw in the width direction, each of the downstream main moving cylinder and the downstream main shifting cylinder being a hydraulic cylinder, characterized in that the downstream main vise mechanism is configured such that a thrust force of the downstream main shifting cylinder toward one side in the width direction is made equal to a thrust force of the downstream main moving cylinder toward another side in the width direction, wherein a position in the width direction where a vise surface of the second of the feed vise jaws (21, 23) is located when the feed vise shifting cylinder reaches a stroke end on an extended side thereof serves as a vise reference position, and wherein the downstream main vise mechanism is configured to locate, if a leading end portion of the workpiece curves, the vise surface of the second downstream main vise jaw at the one side or the other side of the vise reference position in the width direction according to a curvature of the leading end portion of the workpiece when the portion (Wf) correspondent to the product in the workpiece is clamped by cooperation of the first and second downstream main vise jaws (77, 79).