According to modern seismic codes such as Eurocode 8, pile foundations in earthquake-prone areas must resist two different, yet simultaneous bending actions resulting from kinematic and inertial interaction. Due to the different nature of the two demands, pile must resist seismic actions following different patters, thus leading to different design requirements. In this work, analytical solutions are presented to define maximum and a minimum pile diameters required to resist kinematic and inertial effects in an essentially elastic manner, respectively. It is shown that the range of admissible diameters decreases with decreasing soil stiffness and with increasing design acceleration, collapsing into a single admissible diameter for certain problem configurations. Regions where no pile diameter can guarantee elastic response during strong seismic shaking are identified