We study two-parametric families of spatial orbits given in the solved form \(f(x,y,z)=c_{1}\) , \(g(x,y,z)\) = \(c_{2}\) ( \(c_{1}\) , \(\; c_{2}\) =const) which are produced by three-dimensional potentials \(V=V(x,y,z)\) inside a material concentration. These potentials have to satisfy two linear partial differential equations (PDEs) which are the basic equations of the 3D Inverse Problem of Newtonian Dynamics and the well-known “Poisson’s equation.” The functions f and g are represented uniquely by the “slope functions” \(\alpha (x,y,z)\) and \(\beta (x,y,z)\) . A suitable class of potentials for this case are the separable ones in Cartesian coordinates, i.e., potentials of the form \(V=P(x)+Q(y)+R(z)\) which have applications in many physical problems. For the given density function \(\rho =\rho (x, y, z)\) \(\rho =\rho _{0}=const.\) , \(\rho =\rho (x)\) , \(\rho =\rho (y)\) , or, \(\rho =\rho (z)\) and a preassigned family of orbits, planar, or three-dimensional potentials producing this family of orbits are found. Proceeding more, we study the 3D harmonic oscillator and the Henon-Heiles potential in three dimensions, and we examine families of orbits compatible with them. The families of straight lines in 3D space are also considered.