Tremendous advances have taken place over the last few years in the field of material science. Material characterization has become an important and powerful research tool in physics. This book aims at answering and explaining some of the problems on anharmonic properties of crystals through a multipronged approach. An effort has been made for obtaining the higher order elastic constants and allied parameters for uranium and thorium mono-chalcogenides. Taking the nearest neighbor distance and hardness parameter as the input data second, third and fourth order elastic constants were computed at various temperatures and used to obtain the first and second order pressure derivatives and partial contractions. These details have been used to discuss the anharmonic properties of solids. The analysis should help shed some light on this important and exciting ground of material characterization, and should be particularly suitable to professionals in this field, or anyone else who may be considering utilizing this data for further studies.