Embedded Block Coding with Optimal Truncation (EBCOT) is the fundamental and computationally very demanding part of the compression process of JPEG2000 image compression standard. EBCOT itself consists of two tiers. In Tier-1, image samples are compressed using context modeling and arithmetic coding. Resulting bit-stream is further formated and truncated in Tier-2. JPEG2000 has a number of applications in various fields where the processing speed and/or latency is a crucial attribute and the main limitation with state of the art implementations. In this paper we propose a new parallel approach to EBCOT context modeling that truly exploits massively parallel capabilities of modern GPUs and enables concurrent processing of individual image samples. Performance evaluation of our prototype shows speedup 12 times for the context modeller, and 1.4--5.3 times for the whole EBCOT Tier-1, which includes not yet optimized arithmetic coder.