The mechanical efficiency of a plant to resist external forces such as gravity (biomass), wind and rain water depends on the characteristic relationship between its form (morphology), material structure (anatomy) and function. Previous studies have shown that this relationship for coconut palms (monocotyledonous plant) significantly differs from hardwood or softwood (dicotyledonous plants) and even from other palm species. The coconut stem tissue (also referred to as "cocowood") has a non-uniform orientation of fibrovascular bundles and density distribution, likely influencing the coconut palm's mechanical properties and capacity to withstand extreme weather conditions without failure. The present study aims at quantifying and characterising the compressive strength and stiffness within the stem green tissue of senile coconut palms (80 to 100 year old) cut from the Pacific islands of Fiji and Samoa. This paper presents results gained from 69 compressive tests carried out on 54 green cocowood small-clear samples. Furthermore, this paper analyses the relationships between the measured mechanical properties and basic density.