We present the first detailed spatio-kinematical analysis and modelling of the planetary nebula Abell 65, which is known to host a post-common envelope, binary, central star system. As such, this object is of great interest in studying the link between nebular morphology and central star binarity. [OIII]5007A and H-alpha+[NII]6584A longslit spectra and imagery of Abell 65 were obtained with the Manchester Echelle Spectrometer on the 2.1-m telescope at the San Pedro Martir Observatory (MES-SPM). Further [OIII]5007A longslit spectra were obtained with the Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope (VLT-UVES). These data were used to develop a spatio-kinematical model for the [OIII]5007A emission from Abell 65. A "best-fit" model was found by comparing synthetic spectra and images rendered from the model to the data. The model comprises an outer shell and an inner shell, with kinematical ages of 15000 +/- 5000 yr kpc^-1 and 8000 +/- 3000 yr kpc^-1, respectively. Both shells have peanut-shaped bipolar structures with symmetry axes at inclinations of 55 +/- 10 deg (to the line-of-sight) for the outer shell and 68 +/- 10 deg for the inner shell. The near-alignment between the nebular shells and the binary orbital inclination (of 68 +/- 2 deg) is strongly indicative that the binary is responsible for shaping the nebula. Abell 65 is one of a growing number of planetary nebulae (seven to date, including Abell 65 itself) for which observations and modelling support the shaping influence of a central binary.