Electrospinning produces continuous fibres with diameters from single nanometres to microns by jetting polymer solutions in high electric fields. Electrospun non-woven filamentary materials attract rapidly growing interest for broad range of applications. Properties of these materials depend on their nano-and microstructure that is determined in turn by the electric field and nanofibre collector. Despite critical importance, deposition of electrospun fibres on substrates has not yet been extensively studied theoretically and new methods of nanofibre collection continue to be developed mostly empirically. The objective of this Letter was to develop and demonstrate numerical simulation of electrospun nanofibre deposition on moving collectors. A dynamic model of nanofibre deposition onto a fast rotating drum was developed and used to simulate partial nanofibre alignment on this collector. The results were compared with the filamentary deposits in two classical stationary collection methods. Good agreement with experimental observations demonstrated predictive ability of simulations. The developed models can be used for the analysis of mechanisms of fibre deposition and alignment on substrates in various electric fields. Better understanding of dynamic nanofibre interaction with the electric field and collectors can lead to improved collector devices enabling one-step integrated nanomanufacturing of the designer nanofilamentary assemblies and architectures.