The well-recognized Lac repressor protein (LacI) regulates transcription by bending DNA into a loop. In addition to the known role of DNA flexibility, there is accumulating evidence suggesting that the flexibility of LacI also plays a role in this gene regulation. Here we extend our elastic rod model for DNA (previously used to model DNA only) to represent LacI. Specifically, we represent sites of concentrated flexibility in the protein with flexible elastic rod domains; and we represent relatively rigid domains of the protein with stiff elastic rod domains. Our analysis shows the sensitivity of looping energetics to the degree of flexibility within the protein over a large range of DNA lengths. In addition, we show that the predicted energetically dominant binding topology (A) remains upon introducing protein flexibility.