International and intercultural groups increasingly perform various kinds of knowledge work that require groups to brainstorm or generate new ideas, such as problem solving, intelligence analysis and design. One observation based on the understanding of cultural differences and group idea generation suggests that cultures, or socially shared systems of concepts and practices among communities of people, introduce both benefits and obstacles to intercultural brainstorming. Cultural diversity in concepts and ways of thinking is in general beneficial, while cultural discrepancy in social norms, communication styles and language can be detrimental to idea sharing and brainstorming outcomes. The major goal of this dissertation is to reconcile the tension between the benefits and obstacles of intercultural collaboration. In this dissertation, I investigate how people with different cultural backgrounds communicate to perform brainstorming. I further propose brainstorming support tools accordingly, and evaluate the designs in the contexts of cross-cultural and cross-lingual brainstorming. The dissertation considers that using computers to retrieve and display language-retrieved pictures, which are pictures relevant to the ongoing conversation, can effectively support intercultural brainstorming. As individuals from different cultures vary in terms of how they perceive and interpret image content, the design attempts to present pictures to elicit diverse thoughts from members of intercultural groups. A study confirms the usefulness of this design for American-Chinese intercultural groups. The dissertation further considers to bridge cultures at the language level, using machine translation (MT) to allow group members to produce and read ideas in their native languages. Another study shows that MT supports the production of ideas but not the comprehension of ideas. The results point to the need to further investigate the detailed processes for producing and comprehending ideas in intercultural groups to inform future designs. The dissertation contributes to the understanding of computer-mediated intercultural brainstorming with behavioral studies and design work, and shows the need for technical designs to take understanding of various aspects of culture, such as social and communicative norms, cognition and languages spoken, into consideration.