The paper outlines a procedure to identify the space-and time-dependent external nonstationary load acting on a closed circular cylindrical shell of medium thickness. Time-dependent deflections at several points of the shell are used as input data to solve the inverse problem. Examples of numerical identification of various nonstationary loads, including moving ones are presented. The relationship between the external load and the stress-strain state of the shell is described by the Volterra equation of the first kind. The identification problem is solved using Tikhonov's regularization method and Apartsin's h-regularization method Keywords: cylindrical shell, nonstationary load, inverse problem, Volterra equation of the first kind, regularization methodIntroduction. Publications on nonstationary vibrations of elastic members are very numerous. Noteworthy are recent interesting studies in this field [7][8][9][10][11]14]. There are far fewer publications concerned with so-called inverse problems. The monographs [5,6] formulate several problems to determine the time-dependent components of the loads on various structural members, assuming that their spatial distribution is known and that the result of application of these loads (displacements or strains) in the form of functions of time at some points is known too. These monographs also give a detailed description of purely mathematical studies that actually provide a theoretical basis for solving inverse problems in mathematical physics and solid mechanics. There are also a few papers on inverse problems [12,13,15] which address the nonstationary behavior of deformed objects. The objective of the present paper is to recover not only the time-dependent component of the nonstationary load on a cylindrical shell, but also its distribution over the mid-surface of the shell.1. Let us identify an axisymmetric nonstationary transverse load arbitrarily distributed along the axis of a hinged cylindrical Timoshenko-type shell (Fig. 1). To solve the identification problem, we will use Tikhonov's regularization [3, 6] and Apartsin's h-regularization [1,2]. To solve the inverse, it is first necessary to solve the direct problem, which should be considered as the first, auxiliary stage in solving the identification problem.The reaction of a Timoshenko-type shell of medium thickness to an axisymmetric transverse load is modeled by a system of linear differential equations [4]: