Cook the pasta according to the package directions. Drain and rinse under cold running water.
In a large bowl, combine the pasta, peas, celery, onion, parsley, and tuna.
In a small bowl, whisk together the oil, vinegar, mustard, 1 teaspoon salt, and ¼ teaspoon pepper.
Pour the dressing over the salad and gently toss. Serve at room temperature or chilled.