A method for estimating the magnitude of a back-and-forth-direction force exerted on a tire comprises: using a plurality of strain sensors fixed to a tire sidewall capable of outputting data on the magnitude of a strain occurred at the position of the strain sensor; reading the output data from the strain sensors when come to fixed measuring positions predetermined around the tire rotational axis; in relation to each of the strain sensors at the respective measuring positions, calculating the back-and-forth-direction force as an intermediate result by the use of the data read from the strain sensor and a relational expression, whereby the intermediate results are obtained from the respective strain sensors; and computing a mean value of only the valid intermediate result(s) so as to output it as the estimated magnitude of the force.