The theoretical estimations and numerical simulations of tubular electron beams in both beam and reflex mode of source operation as well as the off-axis ion extraction from a tubular electron beam ion source (TEBIS) are presented. Numerical simulations have been done with the use of the IGUN and OPERA-3D codes. Numerical simulations with IGUN code show that the effective electron current can reach more than 100 A with a beam current density of about 300–400 A/cm2 and the electron energy in the region of several KeV with a corresponding increase of the ion output. Off-axis ion extraction from the TEBIS, being the nonaxially symmetric problem, was simulated with OPERA-3D (SCALA) code. The conceptual design and main parameters of new tubular sources which are under consideration at JINR, MSL, and BNL are based on these simulations.