A very important issue in the nonlinear analysis of complex problems is to keep the solution error under control. This can be conveniently (and usually also most economically) accomplished by the application of the adaptive analysis. Moreover, adaptivity enables to capture modes of failure that would otherwise remain undetected. The key ingredient of the adaptive process is a reliable and accurate error estimation. The residual-based error estimator enables to capture both the material as well as geometrical nonlinearity of the underlying problem and is well suited for a wide range of engineering problems. The error estimator adopted in this study proved to be efficient in terms of the qualitative as well as quantitative error assessment. On the other hand it also proved to be very demanding in terms of the computational times and, specially in the case of nonlocal regularization, also in terms of memory requirements. This makes the adaptive analysis quite expensive when applied in sequential environment. The inherent computational complexity can be reduced by performing the adaptive analysis in parallel. It was shown that the parallelization of the error estimator is straightforward. The crucial issue, however, refers to the dynamic load balancing and related data migration. Although the vitality of the proposed approach was demonstrated on an example, neither the static partitioning with adaptive restart nor the dynamic partitioning with full restart were found satisfactory. Therefore the development of a dynamic load balancing framework (e.g. using the DRAMA  library, or task migration concept) is considered to be the subject of further development.