An internal EGR parameter estimating device comprising: an interval calculating section configured to set a prescribed time period and to divide the prescribed time period into a plurality of intervals that includes an overlap period (OLPRD) in which an intake valve and an exhaust valve are both open in a single cylinder; an interval cross sectional area opening calculating section configured to calculate an interval cross sectional area opening (VAREAn) of a blow-by gas passage formed between an intake port and an exhaust port during the overlap period (OLPRD) for each of the intervals based on a predetermined valve operating characteristic value (CAMPFn); a cross sectional area opening integrating section configured to integrate the interval cross sectional area openings (VAREAn) over the overlap period (OLPRD); and an effective cross sectional area opening calculating section configured to calculate an effective cross sectional area opening (ASUMOL) of the blow-by gas passage over the overlap period (OLPRD) based on integration of the interval cross sectional area openings (VAREAn); an exhaust gas pressure detecting section configured to detect an exhaust gas pressure (Pex) during the overlap period (OLPRD); an intake air pressure detecting section (S401 to S405) configured to detect an intake air pressure (Pin) during the overlap period (OLPRD); and a blow-by gas quantity calculating section configured to calculate a quantity (MRESOL) of blow-by gas that blows between the exhaust port and the intake port during the overlap period (OLPRD) based on at least the exhaust gas pressure (Pex) and the intake air pressure (Pin) and the effective cross sectional area opening (ASUMOL); characterized in that the effective cross sectional area opening calculating section is further configured to create a first array of interval cross sectional area openings (VAREAln) formed by the intake valve and a second array of interval cross sectional area openings (VAREAEn) formed by the exhaust valve such that each of the interval cross sectional area openings (VAREAln, VAREAEn) of each of the first and second arrays correspond to a specific interval; the effective cross sectional area opening calculating section is further configured to select a smaller of two of the interval cross sectional area openings (VAREAln, VAREAEn) from the first and second arrays for each of the intervals as an effective interval cross sectional area opening (VAREAn) for that one of the intervals; and the effective cross sectional area opening calculating section is further configured to calculate the effective cross sectional area opening (ASUMOL) by integrating the effective interval cross sectional area openings (VAREAn) that were selected over the overlap period (OLPRD). an interval calculating section configured to set a prescribed time period and to divide the prescribed time period into a plurality of intervals that includes an overlap period (OLPRD) in which an intake valve and an exhaust valve are both open in a single cylinder; an interval cross sectional area opening calculating section configured to calculate an interval cross sectional area opening (VAREAn) of a blow-by gas passage formed between an intake port and an exhaust port during the overlap period (OLPRD) for each of the intervals based on a predetermined valve operating characteristic value (CAMPFn); a cross sectional area opening integrating section configured to integrate the interval cross sectional area openings (VAREAn) over the overlap period (OLPRD); and an effective cross sectional area opening calculating section configured to calculate an effective cross sectional area opening (ASUMOL) of the blow-by gas passage over the overlap period (OLPRD) based on integration of the interval cross sectional area openings (VAREAn); an exhaust gas pressure detecting section configured to detect an exhaust gas pressure (Pex) during the overlap period (OLPRD); an intake air pressure detecting section (S401 to S405) configured to detect an intake air pressure (Pin) during the overlap period (OLPRD); and a blow-by gas quantity calculating section configured to calculate a quantity (MRESOL) of blow-by gas that blows between the exhaust port and the intake port during the overlap period (OLPRD) based on at least the exhaust gas pressure (Pex) and the intake air pressure (Pin) and the effective cross sectional area opening (ASUMOL); characterized in that the effective cross sectional area opening calculating section is further configured to create a first array of interval cross sectional area openings (VAREAln) formed by the intake valve and a second array of interval cross sectional area openings (VAREAEn) formed by the exhaust valve such that each of the interval cross sectional area openings (VAREAln, VAREAEn) of each of the first and second arrays correspond to a specific interval; the effective cross sectional area opening calculating section is further configured to select a smaller of two of the interval cross sectional area openings (VAREAln, VAREAEn) from the first and second arrays for each of the intervals as an effective interval cross sectional area opening (VAREAn) for that one of the intervals; and the effective cross sectional area opening calculating section is further configured to calculate the effective cross sectional area opening (ASUMOL) by integrating the effective interval cross sectional area openings (VAREAn) that were selected over the overlap period (OLPRD).