A sheet conveying apparatus that restricts conveyance of sheets to a post-processing apparatus which has become incapable of continuing a post-processing operation. The sheet conveying apparatus is communicably connected to the post-processing apparatus that performs post-processing on a sheet bundle formed by sheets. The sheet conveying apparatus includes a conveying unit for conveying sheets and an escape tray for receiving conveyed sheets which are not conveyed to the post-processing apparatus. A value corresponding to the number of sheet bundles formed by conveyed sheets is counted. A CPU circuit section determines based on communication with the post-processing apparatus whether or not the post-processing operation can be continued thereby. When it is determined that the post-processing operation cannot be continued, the CPU circuit section switches the sheet conveying destination from the post-processing apparatus to the escape tray, based on the counted value.