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Research on possibilities in long-term LHC (Large Hadron Collider) upgrade include considerations on replacing the Nb-Ti dipoles with Nb3Sn outserts and inserts made of some high temperature superconductor (HTS) which outperforms conventional superconductors above 20 T. Regarding to this target, the WP7.4 (Very high field insert) in project EuCARD is to construct about 1 m long HTS dipole producing 6 T in background field of 13 T. Since the quench analysis of HTS coils is challenging, e.g., due to slow propagation velocities and possibly ambiguous limit between the normal and superconducting state, two different strategies are developed in parallel to analyse the quench of the small prototype insert. The one is based on propagation velocities and the other on solving heat diffusion equation with finite element method. The very first steps of the development include benchmark calculations with the already existing programs for small Nb-Ti solenoid to guarantee similar starting points for the partners. After this, a quench analysis was performed for an HTS solenoid. In this paper we consider the results of these calculations.