The GeantV project aims to research and develop the next-generation simulation software describing the passage of particles through matter. While the modern CPU architectures are being targeted first, resources such as GPGPU, Intel© Xeon Phi, Atom or ARM cannot be ignored anymore by HEP CPU-bound applications. The proof of concept GeantV prototype has been mainly engineered for CPU's having vector units but we have foreseen from early stages a bridge to arbitrary accelerators. A software layer consisting of architecture/technology specific backends supports currently this concept. This approach allows to abstract out the basic types such as scalar/vector but also to formalize generic computation kernels using transparently library or device specific constructs based on Vc, CUDA, Cilk+ or Intel intrinsics. While the main goal of this approach is portable performance, as a bonus, it comes with the insulation of the core application and algorithms from the technology layer. This allows our application to be long term maintainable and versatile to changes at the backend side. The paper presents the first results of basket-based GeantV geometry navigation on the Intel© Xeon Phi KNC architecture. We present the scalability and vectorization study, conducted using Intel performance tools, as well as our preliminary conclusions on the use of accelerators for GeantV transport. We also describe the current work and preliminary results for using the GeantV transport kernel on GPUs.