Abstract: This paper presents a theory of penetration of fast mode hydromagnetic plane wave into the cylindrically stratified equatorial ionosphere and atmosphere. The fast mode hydromagnetic plane wave is decomposed into cylindrical wave modes. Then the propagation of cylindrical wave modes in cylindrically stratified ionosphere and atmosphere are solved as a two-point boundary value problem. The governing equations are from Maxwell equations. They are a system of four complex first order differential equations. The lower boundary of the solved region is the ground.The upper boundary is the plane of 500km altitude. Above the upper boundary, the wave electric field component along the magnetic field is zero. The wave magnetic field component along the ambient magnetic field satisfy the Bessel equation. Therefore the wave magnetic field component can be decomposed into cylindrical Bessel functions. The wave magnetic field component at the upper boundary are formed by the summation of inward going wave component and outward going wave component. The wave magnetic field is differentiated with respect to r. Then the inward going wave component is expressed in terms of the Bessel function solution and its differentiation. Through the continuation of the electric and magnetic field along the boundary, the boundary conditions are therefore formed. The cylindrical wave modes are composed to give the spatial distribution of the electromagnetic wave fields.