A future shape estimation apparatus includes an insertion section, a shape sensor and an insertion section future shape estimation circuit. The insertion section has flexibility and is to be inserted into an observation target object. The shape sensor detects a bending state of the insertion section and outputs a detection signal. The insertion section future shape estimation circuit estimates a future shape of the insertion section after a predetermined lapse of time based on information acquired from the detection signal output from the shape sensor, and outputs the future shape as future estimation shape information.