A portal-shaped installation car picks up at an assembly location remote from the face of the tunnel an upper part of a tunnel-lining arch on a pallet. It then rides along rails secured to the side of the tunnel to the face location and presses this upper part against the tunnel roof, whereupon the lower tunnel-lining arch parts are secured in place. Thereafter the car returns with the empty pallet to the rear end of the tunnel at the assembly location and deposits this empty pallet to pick up a full pallet carrying another upper arch part. The sequence is then repeated. As each upper arch part is being secured at the face of the tunnel another upper arch part is assembled on the previously deposited empty pallet with the help of a portal crane that also rides on the rails along the sides of the tunnel.