We consider some problems concerning the classical string and the quantum strings which can have the deep physical meaning. We show that there is the asymmetry of the action and reaction in the string motion for the string with the left end fixed and the right end being in periodic motion. We derive also the quantum internal motion of this system. The quantization of the string with the interstitial massive defect is performed. The classical motion of uniformly accelerated string and its relation the Bell paradox is considered. We discuss the relation of this accelerated string to the Bell spaceship paradox involving the Lorentz contraction. It is evident that the acceleration of the string can be caused by gravity and we show that such acceleration causes the different internal motion of the string. Gravity can be described by the string medium in the Newton model of gravity. We show, that in case of the string model of gravity the motion of planets and Moon are oscillating along the classical trajectories In the string model of hadrons the quarks are treated to be tied together by a gluon tube which can be approximated by the tube of vanishing width, or by string. We apply the delta-function form of force to the left side of the string and calculate the propagation of the pulse in the system.