The Internet’s continued rapid growth is creating an untapped environment containing a large quantity of highly competent computing resources suitable for exploitation in existing capacity-constrained and new innovative capability-driven distributed applications. The Grid is a new computing model that has emerged to harness these resources in a manner that fits the problem solving process needs of the computational engineering design community. Their unique requirements have created specific challenges for Grid technologies to bring interoperability, stability, scalability and flexibility, in addition to, transparent integration and generic access to disparate computing resources within and across institutional boundaries. The emergence of maturing open standards based service-oriented (SO) technologies has fulfilled the fundamental requirements of interoperability, leaves a flexible framework onto which sophisticated system architectures may be built, and provides a suitable base for the development of future Grid technologies. The work presented in this thesis is motivated by the desire to identify, understand, and resolve important challenges involved in the construction of Grid-enabled Problem Solving Environments (PSE) using SO technologies. The work explains why they are appropriate for Grid computing and successfully demonstrates the application and benefits of applying SO technologies in the scenarios of Computational Micromagnetics and Grid-enabled Engineering Optimisation and Design Search (Geodise) systems. Experiences achieved through the work can also be of referential value to future application of Grid computing in different areas.