We will report here on the development of parallel adaptive hp schemes for the modeling of two problems. First we will report on the problems of classical linear elastostatics. Secondly we will describe early work on hyperbolic systems arising from a class of geophysical mass flows arising from landslides, avalanches and the like. These flows often have catastrophic consequences and lead to great loss of life. Over the last few years great strides have been made in developing sound mathematical models of these phenomena (see for e.g. the work of Hutter et. al [1] or more recently Ivarson and Denlinger [2]. Accurate numerical modeling of such flows is of great importance in conducting the realistic simulations necessary for a variety of purposes ranging from public safety planning to validation of the models. Developing parallel adaptive hp finite element simulations requires development of suitable data structures (see for e.g.Laszloffy, Long and Patra [4], load balancing schemes and solvers. For the elliptic systems, we will describe some of our recent work on developing reliable and portable solvers using a variety of preconditioners. For the hyperbolic systems we will extend here the work of Bey, Patra and Oden [3], on model hyperbolic systems to create parallel adaptive approximations. The key features of our approach include integrated development of parallel data structures and partitioners using good ordering schemes. Suitable adaptive strategies and residual based error estimators are other highlights of the work. REFERENCES [1] K. Hutter, M. Siegel, S. Savage and Y. Nohguchi, Two dimensional spreading of a granular avalance down an inclined plane Part 1 Theory, Acta Mechanica 100, 37-68, (1993). [2] R. Ivarson and R. Denlinger, Flow of variably fluidized granular masses across threedimensional terrain 1. Couloumb mixture theory Journal Geophysical Research, 106 B1, 537- 552, (2001). [3] K.S. Bey, J. T. Oden and A. Patra A Parallel hp- Adaptive Discontinuous Galerkin Method For Hyperbolic Conservation Laws, in Applied Numerical Mathematics vol. 20, 1996, pp. 321-336. [4] A. Laszloffy, J. Long and A. Patra, ”Simple Data management Schemes and Scheduling Schemes For Managing the Irregularities in Parallel Adaptive hp Finite Element Simulations” Parallel Computing vol 26, 2000, pp.1765-1788.