An exhaust purification device for an internal combustion engine which is provided with: a particulate filter which is arranged inside of an engine exhaust passage for trapping particulate matter which is contained in exhaust gas, which particulate filter is provided with alternately arranged exhaust gas inflow passages and exhaust gas outflow passages and porous partition walls which separate these exhaust gas inflow passages and exhaust gas outflow passages from each other, wherein in each partition wall, a coated zone where a coated layer with an average pore size which is smaller than the average pore size of a partition wall substrate is used to cover the substrate surface and a non-coated zone at the downstream side of the coated zone and where the substrate surface is not covered by the coated layer are defined; the exhaust purification device being characterised by: the pore size of each partition wall being set so that the ash which is contained in the exhaust gas can pass through the partition wall in the non-coated zone, and by: an electronic control unit comprising: a first calculating means for calculating the quantity of particulate matter which is trapped at the non-coated zone, a first judging means for judging if a quantity of particulate matter which is trapped at the non-coated zone is greater than a first allowable upper limit amount, and a particulate matter removing means for performing particulate matter removal control which removes particulate matter from the particulate filter when it is judged that the quantity of particulate matter which is trapped at the non-coated zone is greater than the first allowable upper limit amount. a particulate filter which is arranged inside of an engine exhaust passage for trapping particulate matter which is contained in exhaust gas, which particulate filter is provided with alternately arranged exhaust gas inflow passages and exhaust gas outflow passages and porous partition walls which separate these exhaust gas inflow passages and exhaust gas outflow passages from each other, wherein in each partition wall, a coated zone where a coated layer with an average pore size which is smaller than the average pore size of a partition wall substrate is used to cover the substrate surface and a non-coated zone at the downstream side of the coated zone and where the substrate surface is not covered by the coated layer are defined; the exhaust purification device being characterised by: the pore size of each partition wall being set so that the ash which is contained in the exhaust gas can pass through the partition wall in the non-coated zone, and by: an electronic control unit comprising: a first calculating means for calculating the quantity of particulate matter which is trapped at the non-coated zone, a first judging means for judging if a quantity of particulate matter which is trapped at the non-coated zone is greater than a first allowable upper limit amount, and a particulate matter removing means for performing particulate matter removal control which removes particulate matter from the particulate filter when it is judged that the quantity of particulate matter which is trapped at the non-coated zone is greater than the first allowable upper limit amount. the pore size of each partition wall being set so that the ash which is contained in the exhaust gas can pass through the partition wall in the non-coated zone, and by: an electronic control unit comprising: a first calculating means for calculating the quantity of particulate matter which is trapped at the non-coated zone, a first judging means for judging if a quantity of particulate matter which is trapped at the non-coated zone is greater than a first allowable upper limit amount, and a particulate matter removing means for performing particulate matter removal control which removes particulate matter from the particulate filter when it is judged that the quantity of particulate matter which is trapped at the non-coated zone is greater than the first allowable upper limit amount. an electronic control unit comprising: a first calculating means for calculating the quantity of particulate matter which is trapped at the non-coated zone, a first judging means for judging if a quantity of particulate matter which is trapped at the non-coated zone is greater than a first allowable upper limit amount, and a particulate matter removing means for performing particulate matter removal control which removes particulate matter from the particulate filter when it is judged that the quantity of particulate matter which is trapped at the non-coated zone is greater than the first allowable upper limit amount. a first calculating means for calculating the quantity of particulate matter which is trapped at the non-coated zone, a first judging means for judging if a quantity of particulate matter which is trapped at the non-coated zone is greater than a first allowable upper limit amount, and a particulate matter removing means for performing particulate matter removal control which removes particulate matter from the particulate filter when it is judged that the quantity of particulate matter which is trapped at the non-coated zone is greater than the first allowable upper limit amount.