Artificial synaptic devices that can be stretched similar to those appearing in soft-bodied animals, such as earthworms, could be seamlessly integrated onto soft machines toward enabled neurological functions. Here, we report a stretchable synaptic transistor fully based on elastomeric electronic materials, which exhibits a full set of synaptic characteristics. These characteristics retained even the rubbery synapse that is stretched by 50%. By implementing stretchable synaptic transistor with mechanoreceptor in an array format, we developed a deformable sensory skin, where the mechanoreceptors interface the external stimulations and generate presynaptic pulses and then the synaptic transistors render postsynaptic potentials. Furthermore, we demonstrated a soft adaptive neurorobot that is able to perform adaptive locomotion based on robotic memory in a programmable manner upon physically tapping the skin. Our rubbery synaptic transistor and neurologically integrated devices pave the way toward enabled neurological functions in soft machines and other applications.