The understanding of the plasma dynamics in the scrape-off layer (SOL) of tokamaks is of crucial importance as we approach the ITER era. In this region, particles and heat coming from the core, through turbulent transport, flow along the magnetic field lines and are exhausted to the vessel. The processes taking place in the SOL govern the performance of the entire device, as they determine the impurity dynamics, the recycling level, the peak heat loads at the vessel, and have an important role in setting the overall plasma confinement. In the recent past, a large effort has been devoted to improve the knowledge of plasma turbulent dynamics in the tokamak SOL, achieving significant progress. In the simplest circular limited configuration, electromagnetic fluid turbulence simulations carried out with the Global Braginskii Solver (GBS) [P. Ricci et al, PPCF 2012] have pointed out the mechanisms that regulate the SOL width, the plasma toroidal rotation, and the turbulence regime transition. In the present work we generalize the magnetic geometry of GBS, to perform simulations with elongated plasmas and non-zero triangularity, and we investigate the effects of plasma shaping on tokamak SOL turbulence. Nonlinear simulations are performed, with different values of elongation and triangularity. The turbulence properties are analyzed, and the gradient removal theory [P. Ricci et al, PoP 2013] is used to estimate the SOL width. Thanks to a linear study, we elucidate the mechanisms through which the plasma shaping affects the SOL turbulence.