We present the results for two-loop massive kite master integrals with elliptics in terms of iterated integrals with algebraic kernels. The key ingredients are new integral representations for sunset subgraphs in d = 4 - 2 epsilon and d = 2 - 2 epsilon dimensions together with differential equations for considered kite master integrals in A + B epsilon form. The obtained results can be easily generalized to all orders in epsilon-expansion and show that the class of functions defined as iterated integrals with algebraic kernels may be large enough for writing down results for a large class of massive Feynman diagrams. (C) 2020 The Author(s). Published by Elsevier B.V.