Nanorods and nanodisks of Be, Mg, and Ca with different shapes and sizes have been theoretically studied. Stable structures have been identified and their electronic and optical properties have been thoroughly examined by means of Density Functional Theory (DFT), Time Dependent DFT (TDDFT) and Real Time TDDFT (RT-TDDFT) calculations. The derived properties and trends are systematically compared to the corresponding ones of 0D structures revealing the effect of size and dimensionality. On top of that, the possible emergence of plasmonic behavior for intense resonance peaks of larger nanoparticles is also examined with the help of suitable transition contribution maps (TCM) and induced density isosurface plots.