The article describes a computer program, called KINSHIP, that performs componential analysis of kinship terminologies. KINSHIP can produce the guaranteed-simplest analyses, employing a minimum number of features (dimensions) and components in kin term definitions. We give special attention to the problem of multiplicity of componential models, arising from alternative simplest kin term definitions, conforming to one feature set. Two intuitive structural constraints are proposed, reducing the immense number of solutions usually obtained, employing only the previous two simplicity restrictions, to one or a few analyses. Illustrative examples are given in which KINSHIP is applied to kinship systems of the Eskimo (Bulgarian, American English) and Sudanese (Turkish) structural types. For the American (Yankee) system, as described by Goodenough, KINSHIP has discovered the most parsimonious analysis known to us. KINSHIP, with its capabilities to produce all alternative componential analyses--not only the simplest ones--can also be a practical aid to analysts having concerns other than the parsimony of models.