Operation Tractable began at 12:00 on 14 August, when 800 Avro Lancaster and Handley Page Halifax heavy bombers struck German positions along the front. As with Totalize, many of the bombers mistakenly dropped their bombs short of their targets, causing 400 Polish and Canadian casualties. Covered by a smoke screen laid down by their artillery, two Canadian divisions moved forwards. Although their line of sight was reduced, German units still managed to inflict severe casualties on the Canadian 4th Armoured Division, which included its Armoured Brigade commander Brigadier Leslie Booth, as the division moved south toward Falaise. Throughout the day, continual attacks by the Canadian 4th and Polish 1st Armoured Divisions managed to force a crossing of the Laison River. Limited access to the crossing points over the Dives River allowed counterattacks by the German 102nd SS Heavy Panzer Battalion. The town of Potigny fell to Polish forces in the late afternoon.
By the end of the first day, elements of the Canadian 3rd and 4th Divisions had reached Point 159, directly north of Falaise, although they had been unable to break into the town. In order to bolster his offensive, Simonds ordered the Canadian 2nd Infantry Division to move toward the front, with the hope that this reinforcement would be sufficient to enable his divisions to capture the town.
Although the first day's progress was slower than expected, Operation Tractable resumed on 15 August; both armoured divisions pushed southeast toward Falaise. The Canadian 2nd and 3rd Infantry Divisions—with the support of the Canadian 2nd Armoured Brigade—continued their drive south towards the town. After harsh fighting, the 4th Armoured Division captured Soulangy but the gains made were minimal as strong German resistance prevented a breakthrough to Trun.
On 16 August, the Canadian 2nd Infantry Division broke into Falaise, encountering minor opposition from Waffen-SS units and scattered pockets of German infantry. Although it would take two more days to clear all resistance in the town, the first major objective of Operation Tractable had been achieved. Simonds began to reorganize the bulk of his armoured forces for a renewed push towards Trun to close the Falaise Pocket.
The drive for Trun by Polish and Canadian Armoured Divisions began on 16 August, with preliminary attacks in preparation for an assault against Trun and Chambois. On 17 August, both armoured divisions of the Canadian 1st Army advanced. By early afternoon, the Polish 1st Armoured Division had outflanked the 12th SS Panzer Division, enabling several Polish formations to both reach the 4th Armoured Division's objectives and significantly expand the bridgehead northwest of Trun. Stanisław Maczek—the Polish divisional commander—split his forces into three battlegroups each of an armoured regiment and an infantry battalion. One of these struck southwest, cutting off Trun and establishing itself on the high ground dominating the town and the Dives river valley, allowing for a powerful assault by the Canadian 4th Armoured Division on Trun. The town was liberated on the morning of 18 August.
As Canadian and Polish forces liberated Trun, Maczek's second armoured battlegroup manoeuvred southeast, capturing Champeaux and anchoring future attacks against Chambois across a 6-mile (9.7 km) front. At its closest, the front was 4 miles (6.4 km) from forces of the U.S. V Corps in the town. By the evening of 18 August, all of Maczek's battlegroups had established themselves directly north of Chambois (one outside of the town, one near Vimoutiers and one at the foot of Hill 262).