Stretchable and conformable synapse memristors that can emulate the behaviour of the biological neural system and well adhere onto the curved surfaces simultaneously are desirable for the development of imperceptible wearable and implantable neuromorphic computing systems. Previous synapse memristors have been mainly limited to rigid substrates. Herein, a stretchable and conformable memristor with fundamental synaptic functions including potentiation/depression characteristics, long/short-term plasticity (STP and LTP), "learning-forgetting-relearning" behaviour, and spike-rate-dependent and spike-amplitude-dependent plasticity is demonstrated based on highly elastic Ag nanoparticle-doped thermoplastic polyurethanes (TPU : Ag NPs) and polydimethylsiloxane (PDMS). The memristor can be well operated even at 60% strain and can be well conformed onto the curved surfaces. The formed conductive filament (CF) obtained from the movement of Ag nanoparticle clusters under the locally enhanced electric field gives rise to resistance switching of our memristor. These results indicate a feasible strategy to realize stretchable and conformable synaptic devices for the development of new-generation artificial intelligence computers.