An in-mold solidified shell thickness estimation apparatus comprising: an input device configured to receive an input of: a measurement result of a temperature of molten steel in a tundish of a continuous casting facility; measurement results of a width of a strand being cast and of a casting speed in the continuous casting facility; measurement results of a temperature of a mold copper plate and of an amount of heat removed from a mold in the continuous casting facility; and input values of a chemical composition of the molten steel and of the thickness of the strand; a model database configured to store a model formula and a parameter related to a solidification reaction of the molten steel inside the mold of the continuous casting facility; and a heat transfer model calculator configured to estimate an in-mold solidified shell thickness by calculating temperature distributions of the mold and of the molten steel inside the mold by solving a three-dimensional unsteady heat transfer equation using: the measurement result of the temperature of the molten steel in the tundish of the continuous casting facility, the measurement results of the width of the strand being cast and of the casting speed in the continuous casting facility, the measurement results of the temperature of the mold copper plate and of the amount of heat removed from the mold in the continuous casting facility, and the input values of the chemical composition of the molten steel and of the thickness of the strand, and the model formula and the parameter, wherein the heat transfer model calculator is configured to correct errors in the temperature of the mold copper plate and in the amount of heat removed from the mold, by correcting an overall heat transfer coefficient between the mold copper plate and the solidified shell. an input device configured to receive an input of: a measurement result of a temperature of molten steel in a tundish of a continuous casting facility; measurement results of a width of a strand being cast and of a casting speed in the continuous casting facility; measurement results of a temperature of a mold copper plate and of an amount of heat removed from a mold in the continuous casting facility; and input values of a chemical composition of the molten steel and of the thickness of the strand; a measurement result of a temperature of molten steel in a tundish of a continuous casting facility; measurement results of a width of a strand being cast and of a casting speed in the continuous casting facility; measurement results of a temperature of a mold copper plate and of an amount of heat removed from a mold in the continuous casting facility; and input values of a chemical composition of the molten steel and of the thickness of the strand; a model database configured to store a model formula and a parameter related to a solidification reaction of the molten steel inside the mold of the continuous casting facility; and a heat transfer model calculator configured to estimate an in-mold solidified shell thickness by calculating temperature distributions of the mold and of the molten steel inside the mold by solving a three-dimensional unsteady heat transfer equation using: the measurement result of the temperature of the molten steel in the tundish of the continuous casting facility, the measurement results of the width of the strand being cast and of the casting speed in the continuous casting facility, the measurement results of the temperature of the mold copper plate and of the amount of heat removed from the mold in the continuous casting facility, and the input values of the chemical composition of the molten steel and of the thickness of the strand, and the model formula and the parameter, wherein the measurement result of the temperature of the molten steel in the tundish of the continuous casting facility, the measurement results of the width of the strand being cast and of the casting speed in the continuous casting facility, the measurement results of the temperature of the mold copper plate and of the amount of heat removed from the mold in the continuous casting facility, and the input values of the chemical composition of the molten steel and of the thickness of the strand, and the model formula and the parameter, wherein the heat transfer model calculator is configured to correct errors in the temperature of the mold copper plate and in the amount of heat removed from the mold, by correcting an overall heat transfer coefficient between the mold copper plate and the solidified shell.