Abstract: A tire burst predicting device which can predict occurrence of bursting of a tire and gives an alarm properly is provided. A break point frequency is estimated on the basis of time series data of wheel speed detected at a wheel speed sensor from frequency response of a first order model to which a transmission characteristic from a road surface disturbance to a wheel speed is approximated. A braking force gradient corresponding to the estimated break point frequency is estimated, on the basis of a map, which is prestored, representing a relationship between break point frequencies and braking force gradients. Extra high frequency components are eliminated from the estimated braking force gradient by a low pass filter to reduce estimation dispersion. Differentiators detect changing speed of the braking force gradient. An alarm is given when there is a possibility of bursting of tire when the detected changing speed reaches or exceeds a predetermined threshold value.