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We present a continuous analytic current-voltage (I-V) model for cylindrical undoped (lightly doped) surrounding gate (SGT) MOSFETs. It is based on the exact solution of the Poisson's equation, and the current continuity equation without the charge-sheet approximation, allowing the inversion charge distribution in the silicon film to be adequately described. It is valid for all the operation regions (linear, saturation, subthreshold) and traces the transition between them without fitting parameters, being ideal for the kernel of SGT MOSFETs compact models. We have demonstrated that the I-V characteristics obtained by this model agree with three-dimensional numerical simulations for all ranges of gate and drain voltages.