It has been known that the emission from row crops strongly depends on the direction of vegetation row structures relative to the polarization of radiometric receiving antenna. The purpose of the paper is to develop an emission model to interpret the existing emission data of row crop canopy and to aid in understanding the emission process for a row structured vegetation layer or other anisotropically-emitting medium. The vegetation layer of row crops is modelled as a random slab embedded with small thermally emitting spheroids with major axis aligned parallel to the row crop direction. The effects of geometric row structure of vegetation layer can be accounted for by assuming that each thermally-emitting object such as a leaf is aligned to a certain preferred direction. The vegetation canopy is a tenuous medium at microwave frequency so that it is possible to use the radiative transfer theory in emission model. The total emission from the canopy is given in a simple algebraic form based on the zero-order radiative transfer theory. The single scattering albedo for a spheroid and its phase function are derived in order to use in the radiative transfer-based emission computation. The effects of layer azimuthal dependence on emission are accounted for by using an anisotropic albedo in the transfer theory. The developed emission theory favourably compares with the brightness temperature measured over the soybeans canopy, and verifies that a maximum emission reception occurs when the receiving antenna polarization state is perpendicular to the row direction. The emission theory may also find applications in the interpretation of optical and infrared emission data taken from an anisotropic thermal medium.