Amplitude and phase problems in physical research are examined. The construction of methods and algorithms for solving amplitude and phase problems is analyzed without drawing on additional information about the signal and its spectrum. Mathematical models of amplitude and phase problems are proposed for the case of one- and two-dimensional continuous signals and approximate methods are found for solving them. The models are based on using nonlinear singular and bisingular integral equations. The amplitude and phase problems are modeled by corresponding nonlinear singular and bisingular integral equations defined on the numerical axis (in the one-dimensional case) and on the plane (in the two-dimensional case). The constructed nonlinear singular and bisingular integral equations are solved using spline-collocation methods and the method of mechanical quadratures. The systems of nonlinear algebraic equations yielded by these methods are solved by a continuous method for solving nonlinear operator equations. A model example demonstrates the effectiveness of the proposed method for solving the phase problem in the two-dimensional case.