In many diverse fields, the measurements are directions- A biologist may be interested in the direction of flight of the bird or orientation of an animal while geologist may be measuring the direction of earth''s magnetic field. Such directions may be in two or three dimensions. A set of such observations on the directions is referred to as ‘directional data''. In particular analysis pertaining to two dimensional directional data falls under the topic ‘CIRCULAR STATISTICS''. For such data, circular models such as Wrapped Normal, Wrapped Cauchy, von Mises and Cardioid etc. are constructed and inference procedures were studied. A little attention is paid to construct circular models corresponding to life testing models and other important models like Half Logistic and Binormal distributions. Hence the present work is concerned with construction of new circular models and suggested a method of generating family of new circular models. This work motivates budding scholars to do further extensions and helps practitioners to use them for new applications.