We present a method to constrain galaxy parameters directly from three-dimensional data cubes. The algorithm compares directly the data with a parametric model mapped in $x,y,lambda$ coordinates. It uses the spectral lines-spread function (LSF) and the spatial point-spread function (PSF) to generate a three-dimensional kernel whose characteristics are instrument specific or user generated. The algorithm returns the intrinsic modeled properties along with both an `intrinsic model data cube and the modeled galaxy convolved with the 3D-kernel. The algorithm uses a Markov Chain Monte Carlo (MCMC) approach with a nontraditional proposal distribution in order to efficiently probe the parameter space. We demonstrate the robustness of the algorithm using 1728 mock galaxies and galaxies generated from hydrodynamical simulations in various seeing conditions from 0.6 to 1.2. We find that the algorithm can recover the morphological parameters (inclination, position angle) to within 10% and the kinematic parameters (maximum rotation velocity) to within 20%, irrespectively of the PSF in seeing (up to 1.2) provided that the maximum signal-to-noise ratio (SNR) is greater than $sim3$ pixel$^{-1}$ and that the ratio of the galaxy half-light radius to seeing radius is greater than about 1.5. One can use such an algorithm to constrain simultaneously the kinematics and morphological parameters of (nonmerging) galaxies observed in nonoptimal seeing conditions. The algorithm can also be used on adaptive-optics (AO) data or on high-quality, high-SNR data to look for nonaxisymmetric structures in the residuals.
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