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In this paper, we present the design and the expected performance of the classical Lyot coronagraph for the high contrast imaging modes of the wide-field imager MICADO. MICADO is a near-IR camera for the Extremely Large Telescope (ELT, previously E-ELT), with wide-field, spectroscopic and coronagraphic capabilities. MICADO is one of the first-light instruments selected by the ESO. Optimized to work with a multi-conjugate adaptive optics corrections provided by the MOARY module, it will also come with a SCAO correction with a high-level, on-axis correction, making use of the M4 adaptive mirror of the telescope. After presenting the context of the high contrast imaging modes in MICADO, we describe the selection process for the focal plane masks and Lyot stop. We will also show results obtained in realistic conditions, taking into account AO residuals, atmospheric refraction, noise sources and simulating observations in angular differential imaging (ADI) mode. Based on SPHERE on-sky results, we will discuss the achievable gain in contrast and angular separation provided by MICADO over the current instruments on 10-m class telescopes, in particular for imaging young giant planets at very short separations around nearby stars as well as planets on wider orbits around more distant stars in young stellar associations., Comment: 10 pages, 5 figures, AO4ELT 5 conference proceeding