A substrate polishing device for polishing a quadrilateral-shaped substrate, the substrate polishing device comprising: a surface plate; a substrate support mechanism that is attached to the surface plate and that is configured to support the substrate; a polishing head mechanism for attaching a polishing pad, the polishing head mechanism opposing the surface plate; and an orbital drive mechanism for orbitally driving the polishing head mechanism, and a first pressure control mechanism and a second pressure control mechanism; wherein the substrate support mechanism comprises: a base plate; a plurality of plate flow passages provided in the base plate; and a plurality of substrate support chambers provided so as to oppose the back surface of the substrate, wherein each substrate support chamber is connected to one of the plurality of plate flow passages, and wherein each of the plurality of plate flow passages is in communication with the first pressure control mechanism which is configured to control an internal pressure of each of the plurality of substrate support chambers independent from an internal pressure of the other substrate support chambers; wherein the polishing head mechanism comprises: a polishing head main body; a plurality of head flow passages provided in the polishing head main body; and a plurality of plurality of polishing pad support chambers provided so as to oppose the back surface of the polishing pad, wherein each polishing pad support chamber is connected to one of the plurality of head flow passages, and wherein each head flow passage is in communication with the second pressure control mechanism which is configured to control an internal pressure of each of the plurality of polishing pad support chambers independent from an internal pressure of the other polishing pad support chambers. a surface plate; a substrate support mechanism that is attached to the surface plate and that is configured to support the substrate; a polishing head mechanism for attaching a polishing pad, the polishing head mechanism opposing the surface plate; and an orbital drive mechanism for orbitally driving the polishing head mechanism, and a first pressure control mechanism and a second pressure control mechanism; wherein the substrate support mechanism comprises: a base plate; a plurality of plate flow passages provided in the base plate; and a plurality of substrate support chambers provided so as to oppose the back surface of the substrate, wherein each substrate support chamber is connected to one of the plurality of plate flow passages, and wherein each of the plurality of plate flow passages is in communication with the first pressure control mechanism which is configured to control an internal pressure of each of the plurality of substrate support chambers independent from an internal pressure of the other substrate support chambers; wherein the polishing head mechanism comprises: a polishing head main body; a plurality of head flow passages provided in the polishing head main body; and a plurality of plurality of polishing pad support chambers provided so as to oppose the back surface of the polishing pad, wherein each polishing pad support chamber is connected to one of the plurality of head flow passages, and wherein each head flow passage is in communication with the second pressure control mechanism which is configured to control an internal pressure of each of the plurality of polishing pad support chambers independent from an internal pressure of the other polishing pad support chambers. a base plate; a plurality of plate flow passages provided in the base plate; and a plurality of substrate support chambers provided so as to oppose the back surface of the substrate, wherein each substrate support chamber is connected to one of the plurality of plate flow passages, and wherein each of the plurality of plate flow passages is in communication with the first pressure control mechanism which is configured to control an internal pressure of each of the plurality of substrate support chambers independent from an internal pressure of the other substrate support chambers; wherein the polishing head mechanism comprises: a polishing head main body; a plurality of head flow passages provided in the polishing head main body; and a plurality of plurality of polishing pad support chambers provided so as to oppose the back surface of the polishing pad, wherein each polishing pad support chamber is connected to one of the plurality of head flow passages, and wherein each head flow passage is in communication with the second pressure control mechanism which is configured to control an internal pressure of each of the plurality of polishing pad support chambers independent from an internal pressure of the other polishing pad support chambers. a polishing head main body; a plurality of head flow passages provided in the polishing head main body; and a plurality of plurality of polishing pad support chambers provided so as to oppose the back surface of the polishing pad, wherein each polishing pad support chamber is connected to one of the plurality of head flow passages, and wherein each head flow passage is in communication with the second pressure control mechanism which is configured to control an internal pressure of each of the plurality of polishing pad support chambers independent from an internal pressure of the other polishing pad support chambers.