Use of Lagrangian vortex particle methods (VPMs) can be considered as efficient approach to solving actual engineering problem, mainly connected with prediction of unsteady hydrodynamic loads acting on the structures in the flow, including coupled fluid-structure interaction (FSI) problems. VPMs for 2D flows simulation are developed much better in comparison to 3D case; however, even 2D simulations can be useful in practical applications, mainly connected with industrial aerohydrodynamic problems (wind loads for buildings and structures, stream loads for underwater pipelines, cables, etc). Quasi-3D simulations are performed often, considering flat flows around cross-sections of the structures that has high elongation. The VM2D code (https://github.com/vortexmethods/VM2D) is developed by authors that makes it possible to perform simulations of viscous incompressible media by using separate vortex particles for vorticity transfer simulation and viscous vortex domains method for diffusive processes reproduction. In order to improve classical well-known approach, new models and numerical algorithms are implemented for the boundary integral equation solution that describes vorticity generation on the contour. For FSI problems stable semi-implicit coupling scheme is implemented that allows for considering airfoils with arbitrary masses, up to very small. Since each vortex particle has long-range influence, all computational subroutines being implemented “straightforwardly”, have quadratic computational cost with respect to number of vortex particles or number of panels on the body’s contour or surface. To overcome this issue, fast methods with quasi-linear numerical complexity are suggested, and they are adapted for computations on GPU. For 3D flows simulation the so-called “closed vortex loops” method is developed and implemented in the VM3D code, that has similar structure with the obvious note, that 3D algorithms normally are much more complicated in comparison to 2D ones. Number of model problems are considered, the results of numerical simulation are in good agreement with known experimental or numerical data.