An impact and vibration-resistant noise filter avoiding cracking of a core at the time of application of a vibration or impact. The noise filter includes a case and core. The case has a first case portion having a first wall portion, a second wall portion, and a first bottom wall portion. The first and second wall portions have first and second parting surfaces, respectively on the end surfaces thereof. The first bottom wall portion is positioned between the first and second wall portions. A first supporting piece 31B, whose base end is positioned on the side of the first bottom wall portion and whose free end extends toward the first parting surface, is formed on the first wall portion. Similarly, a second supporting piece is formed in the second wall portion. First and second presser pieces are formed respectively on the first and second bottom wall portions. The core is resiliently retained by the first and second supporting pieces, and first and the second presser pieces.