For the detailed investigation of the 3D unsteady incompressible viscous separated fluid flows around a sphere (for 200 ≤ Re ≤ 700) and a circular cylinder (for 200 ≤ Re ≤ 400) the direct numerical simulation and 3D visualization are used. For 3D visualization of the fluid flows around a sphere the definition of vortex core as a connected region containing two negative eigenvalues of the S^2 + Ω^2 tensor is used (where S_{i,j} and Ω_{i,j} are the rate of strain and the rate of rotation tensors). The formation mechanism of vortices in the sphere wake for Re = 500 is described in detail. For 3D visualization of the fluid flows around a circular cylinder the 3D isosurfaces of the streamwise component of vorticity ω_x are used.