We propose a novel data model and its language for querying object-oriented databases where objects may hold spatial, temporal or constraint data, conceptually represented by linear equality and inequality constraints. The proposed LyriC language is designed to provide a uniform and flexible framework for diverse application realms such as (1) constraint-based design in two-, three-, or higher-dimensional space, (2) large-scale optimization and analysis, based mostly on linear programming techniques, and (3) spatial and geographic databases. LyriC extends flat constraint query languages, especially those for linear constraint databases, to structurally complex objects. The extension is based on the object-oriented paradigm, where constraints are treated as first-class objects that are organized in classes. The query language is an extension of the language XSQL, and is built around the idea of extended path expressions. Path expressions in a query traverse nested structures in one sweep. Constraints are used in a query to filter stored constraints and to create new constraint objects.