Goal. Development of the generalized physical principle of development of plasma channel of a high-voltage electrical pulse spark discharge in the homogeneous dielectric of the different aggregate state. Methodology. Basis of physical optics, theoretical electrical engineering, electrophysics bases of technique of high-voltage and large pulse currents, bases of high-voltage pulse technique and measuring technique. Results. Development of physical principle of development of plasma channel of an electric pulse spark discharge is executed in a homogeneous gas dielectric on the applied example of the use in calculations and experiments of the double-electrode discharge system (DEDS) with a long air interval, testing action of standard interconnect аperiodic pulse of high-voltage of temporal shape of Tm/Тd≈200 μs/1990 μs of positive polarity. The generalized formula is got for the calculation of total length of lc of the real way of development of an pulse spark discharge in an air dielectric, which allowed to formulate the offered physical principle in the following kind: «The plasma channel of an pulse spark discharge in a gas dielectric spreads from one of its points to other after a way length of lc, providing the least falling on it of electric voltage of Uc». It is shown that this principle in the first approaching can be applied and to the homogeneous liquid and hard dielectrics. Comparison of the developed physical principle of distribution of plasma channel of an electrical spark discharge is executed in a dielectrical environment with fundamental Fermat physical principle (a law) for distribution of light in an optically transparent environment, which specifies on mathematical likeness and closeness on destiny of these physical principles. Calculation estimations of falling of electric voltage of Uc on total length of lc of the real zigzag way of development in the air dielectric of DEDS a «edge-plane» with the least length of its discharge interval of lmin=1,5 m is presented, that a value Uc does not exceed 9 % from the experimental level of aggressive voltage of Umd≈611,6 кV in this DEDS for the аperiodic pulse of voltage of Tm/Тd≈200 μs/1990 μs. It is set that the estimated time of td advancement of leader channel of electric pulse discharge in air DEDS (lmin=1,5 m) on its real way total length of lc≈1,53 m makes td≈15,3 μs, and experimental duration of cut of Tdc of the indicated аperiodic impulse of voltage utilized in experiments, characterizing time of short circuit by the plasma channel of discharge of air interval in DEDS, appears equal Тdc≈td≈17 μs. Originality. The generalized physical principle of development of plasma channel of a high-voltage electrical pulse spark discharge is first developed in the homogeneous dielectric of the different aggregate state. Practical value. Application in electrical engineering practice and high-voltage pulse technique of the offered principle of distribution in the dielectrics of plasma channel of an pulse spark discharge will allow to develop both new and to perfect the existent methods of computer design of electro-discharge processes in the gas, liquid and hard insulation of different high-voltage electrical power engineering and electrophysics devices, directed on the increase of reliability of their operation.