The study tested the problem of optimal control of ion beam etching to minimize geometric dimensions of the etched elements. This problem is solved by changing the angle of incidence of the ion beam in relation to the target (IBE method). Advanced techniques for creating embossing functional layers, including various ways of dry etching, are necessary for making chips with submicron elements. One of those ways is the ion-beam etching (IBE) based on the action of mono electric ion beams. It permits to change the angle of the target in relation to the ion beam, thereby to control the angle of the etched elements. One of the advantages of IBE is the availability of sufficiently accurate mathematical model. Evolution of the freeform surface during ion beam etching is described by the essentially nonlinear hyperbolic equation of the first order. The paper describes the function that determines the angle formed by the beam of the incidence of the ions to the sputtered surface, for two-dimensional and three-dimensional cases. To characterize the degree of drifting geometrical dimensions, we introduced the functional and set the problem of optimal control with non-fixed time. However, due to the special features of the IBE process, we succeeded in bringing the time-fixed problem to the fixed-time one. For this problem, using the technique of singular variations, we established Pontryagin maximum principle. Based on this principle, we designed software package to search for the optimal regimes for different initial profiles. It should be noted, that to search for the optimal control, it is not necessary to solve the adjoint system, which greatly facilitates the computational process. We also examined the IBE process for the semicircular initial mask. For comparison, we performed calculations with the optimal control and without it and made appropriate conclusions.