This thesis deals with a comparative study of arch structures for the geometrically nonlinear buckling load and free vibration using the finite element computer program, MSC/NASTRAN. A good agreement is observed between the results from MSC/NASTRAN software and the relevant literatures. Two main in-plane problems are considered: nonlinear buckling load of inclined arches and large amplitude free vibration of arches supported at the same level. There are four types of arch to be considered : Circular, Parabolic, Sine and Catenary arch. The rise to span ratio of these arches is in the range of 0.10 to 0.50. The inclined ratio ranges from 0.60 to 1.00 and the arches are subjected to the uniformly distributed vertical load along arch axis. The "Arc - Length" method is used for analysis of the buckling load while the nonlinear free vibration is analyzed by applying the direct iteration technique combined with the load translation equivalent approach. From this study, it is found that the inclined ratio has an effect in increasing of the buckling load coefficients. Whereas the results on the degree of nonlinearity show that large amplitude vibration has more effect to the shallow arches than the deep ones and trend to be the softening type of spring.