Estimation of dielectric slab permittivity is considered by using a flared coaxial line. A problem of reflection from a flared coaxial line that radiates into a dielectric slab with a flange is solved. A flared coaxial line is modeled with multiply stepped coaxial lines with different inner and outer conductors. A set of simultaneous equations for the modal coefficients is constituted based on the boundary conditions. Computations are performed to illustrate the reflection behavior in terms of the coaxial line geometry, frequency, and permittivity of a dielectric slab. Nomograms are developed to estimate the permittivity from the measured reflection coefficients. The utility of a flared coaxial line for the determination of slab permittivity is discussed.