We studied the variation of the shape of the proton intensity–time profiles in simulated gradual Solar Energetic Particle (SEP) events with the relative observer’s position in space with respect to the main direction of propagation of an interplanetary (IP) shock. Using a three-dimensional (3D) magnetohydrodynamic (MHD) code to simulate such a shock, we determined the evolution of the downstream-to-upstream ratios of the plasma variables at its front. Under the assumption of an existing relation between the normalized ratio in speed across the shock front and the injection rate of shock-accelerated particles, we modelled the transport of the particles and obtained the proton flux profiles to be measured by a grid of 18 virtual observers located at 0.4 and 1.0 AU, with different latitudes and longitudes with respect to the shock nose. The differences among flux profiles are the result of the way each observer establishes a magnetic connection with the shock front, and we found that changes in the observer’s latitude may result in intensity changes of up to one order of magnitude at the two radial distances considered here. The peak intensity variation with the radial distance for the pair of observers located at the same angular position was also derived. This is the first time that the latitudinal dependence of the peak intensity with the observer’s heliocentric radial distance has been quantified within the framework of gradual SEP event simulations.