In this work the critical indices β, γ , and ν for a three-dimensional (3D) hardcore cylinder composite system with short-range interaction have been obtained. In contrast to the 2D stick system and the 3D hardcore cylinder system, the determined critical exponents do not belong to the same universality class as the lattice percolation,although they obey the common hyperscaling relation for a 3D system. It is observed that the value of the correlation length exponent is compatible with the predictions of the mean field theory. It is also shown that, by using the Alexander-Orbach conjuncture, the relation between the conductivity and the correlation length critical exponents has a typical value for a 3D lattice system. ; The authors are in debt to Alberto Proenc¸a for providing the computational resources (SEARCH) used in this work. J.S. thanks Davide Cellai for a stimulating discussion. The numerical calculations were performed on the Advanced Research Computing Services with HTC/HPC clusters and the SEARCH cluster, financed through the Programa de Reequipamento Cient´ıfico Nacional, FCT-Fundac¸ ˜ao para a Cência e a Tecnologia, CONC-REEQ/443/EEI/2005, and by the Program POCI 2010 funded by FEDER. This work is also funded by FEDER funds through the “Programa Operacional Factores de Competitividade COMPETE” and by the FCT: Project References PTDC/CTM/69316/2006, NANO/NMed-SD/0156/2007, PTDC/EME-PME/108859-2008, and PTDC/CTM-NAN/112574/2009. J.S. is financed through FCT Grant No. SFRH/BD/60623/2009. The authors also acknowledge support from COST Action MP1003 (European Scientific Network for Artificial Muscles) and COST Action MP0902 [Composites of Inorganic Nanotubes and Polymers (COINAPO)].