Summary: We investigate the problem of linear broadcast, which is performed in a network in which messages follow linear routes. This is a characteristic of many high-speed networks, in which a special hardware is used for switching. Following, extending, and improving the recent work of C. T. Chou and I. S. Gopal [Linear Broadcast routing, J. Algorithms 10, 490-517 (1989)], we study cases when the switching hardware has various limitations. We present algorithms that compute an optimal broadcast routing for any given number of linear routes. Our main result is an $$O(N)$$ algorithm for the general problem of linear broadcast routing, for a tree network of size $$N$$, for which an $$O(N^ 2)$$ algorithm was given by Chou and Gopal.