Summary: An artificial spiking neuron model which has a generalized piece-wise constant (ab. PWC) vector field and state-dependent reset is proposed. Advantages of the PWC vector field include simplicity for hardware implementation, easiness to tune parameters, suitability for theoretical analysis based on theories on discontinuous ordinary differential equations (ab. ODEs). Using the analysis techniques of discontinuous ODEs, it is shown that the model can reproduce 6 types of the typical neuron-like responses (neurocomputational properties), the occurrence mechanisms of which have qualitative similarities to those of Izhikevich’s simple neuron model.