The main objective of this paper is to elaborate effective numerical methods for analyzing liquid vibrations in partially filled rigid reservoirs with baffles under coupled action of vertical and horizontal excitations. The novelty of the proposed approach consists in involving the fuzzy logic concepts for estimating uncertainties in loading parameters. It is supposed that the load frequencies and amplitudes are characterized by triangular fuzzy numbers. First, the crisp boundary value problem is formulated for receiving own modes and frequencies of the liquid vibrations in the reservoirs without baffles, with circular horizontal, and vertical baffles. After receiving the solutions of these spectral problems by boundary element methods, the forced vibrations of liquid are considered. Modes, obtained at solving the spectral problems are used onwards as basic functions in series for an unknown potential and a free surface elevation. The forced vibrations are considered in a weakly nonlinear formulation, that leads to second order differential equations relative to generalized coordinates. Using the triangular fuzzy numbers for describing uncertainties in initial data, the fuzzy initial value problem is reduced to a system of fuzzified differential equations. The numerical solution of this system has been received and analyzed.