Effective shell finite elements are of utmost interest in engineering practice, and more particularly triangular shell elements are often needed to handle complex geometries. The quadrilateral elements of the MITC family have been shown to be effective for general asymptotic behaviors, but a triangular MITC shell finite element of comparable performance remains to be found. The main difficulty is to reduce the locking phenomenon arising in bending dominated situations without destroying the ability of the procedure to accurately capture membrane dominated and mixed behaviors. In this context, we have designed a simple numerical rank test aimed at assessing the reliability of MITC triangular elements. This test led to selecting some specific MITC6 tying schemes, which have been further assessed using some meaningful test problems. The assessment results showed that the MITC6a shell element is a most promising candidate, although it may feature some non-physical membrane spurious modes in some specific shell problems.