Tactile object shapes are considered as important properties in robotic manipulation. Many researches have focused recently on using tactile sensing systems to enable tactile information processing in robotics. Spiking Neural Networks (SNNs) are emerging as promising methods alternative to deep learning due to their ability to process information in an event-driven manner. In this paper, we propose a SNN architecture and hardware implementation for tactile object shapes recognition. The network is fed by an array of 160 piezoresistive tactile sensors where the object shapes are applied. Results demonstrate that the proposed system is able to discriminate the tactile object shapes with 100% accuracy on unseen data having time steps up to 0.1 ms. Moreover, the network has been implemented on a Raspberry Pi platform achieving real time classification.