Modeling and simulations devoloped for examining the physiological structures and dynamical behaviours of the neurons are of importance in terms of supporting the experimental studies. In this study the electrical theory of excitation propagation in excitable cell was investigated. The basic principals of linear cable theory were given and general differential equations concerning excitable cells were derived. The passive cable model simulation of neuron was made through the programme of MATLAB(7.0.4)/Simulink. In order to reach the realistic model, which is one of the main targets of the study, two simplified and revised models were used. A realistic wave shape was produced in MATLAB(7.0.4)/Simulink as the action potential wave shape spreading in neuron. They are as expected in the simplified model. When the simulation results of the two simplified and revised models compared, in the output of the revised model the minimum amplitude is seen to decrease. In the revised model, an ideal capacity element which we recommend was found.