Car parking questions keep cropping up every now and then, and most people assume that parking in downtown area is very difficult and also very expensive. In reality, there is plenty of parking, both on-street parking (remember your parking spot number and you can pay at any pay station around downtown) and many parking lots, both open air and covered, with most office buildings also offering public parking. It is not recommended to park in the open air parking lots overnight since there is no attendant.

Parking rates are not particularly expensive when compared to other major cities of North America -- prices vary from around $12 to over $20 for 24/h, with most lots charging for each 20 or 30 minutes up to the maximum, making on-street parking a cheaper alternative for short-term. Weekend rates are significantly cheaper.

A few suggestions:

1. At the corner of Atwater and  de Maisonneuve they charge C$10 per daytime and additional C$5.50 for staying overnight. Phone (514) 838-1253 to verify.

2. On Mackay between Sainte-Catherine and de Maisonneuve there is another similar lot with same rates.

3. On René-Lévesque at Saint-Mathieu there is another underground parking lot that belongs to Nouvel Hotel and their rates are also the same as above.

4. Under Complexe Desjardins (entrances below the Hyatt on Jeanne Mance Street just before Sainte Catherine, or off Saint-Urban just below Sainte-Catherine), at around $20/24h. This parking lot is in the middle of the Quartier des spectacles (entertainment district) so during the Jazz Festival and other events, prices go up to around $25; check the rates before parking there. Most weekends are at a much lower rate.

5. On Berri between de Maisonneuve and Ontario, there's parking under the new library Bibliothèque nationale, for $12 per 24 hours, $9 on weekends. Parking entrance is off Avenue Savoie.

6. In the Quartier International, close to the W, Intercontinental, and St. James hotels: from Saint-Antoine turn left on Saint-Alexandre (just past Square Victoria) and there's parking under the CDP Building -- 1,300 spaces, security cameras, access to the underground tunnels, and even car wash available. C$23 for 24h.

7. At the Eaton Centre shopping mall, linked to the Fairmont Reine Elizabeth and the rest of the underground city, and convenient to McGill University. Enter on McGill College Avenue between de Maisonneuve and Ste-Catherine Avenues. Posted rate is $20/24h, but two overnights are billed $32.

8. For Old Montreal, see this pdf map of parking lots.

9. For short-term parking, see this pdf map of metered on-street parking (in French only; orange means it's metered parking; green means city-run open-air parking lots). Montreal has four paid on-street parking zones (information on chargeable period, rates and maps in English). Downtown and the Plateau cost $3 per hour and often won't let you pay for more than 2 hours at a time. You can pay at any parking pay station, and no need to return to you car to put your ticket on your dashboard, and the municipal lot hours are from 7:00 a.m. to 10:00 p.m.

10. As an alternative do downtown prices, there is long-term parking by the Longueuil métro albeit uncovered and unmonitored. Only lots 4 and 5 allow stays of more than 24h.

There are some online parking sites such as Best Parking (which also has its smartphone apps) and Parkopedia (which has mobile parking apps on several platforms);. to pay for on-street parking via your mobile phone, see this app although it will cost you $0.40 for the convenience, and given roaming charges, this app is perhaps more useful for residents than tourists. 

And a word on safety: Montreal is a very safe city with a very low crime rate. However, it is not free from car thefts and vandalism, therefore when you park on the streets or in open air parking lots, make sure you lock your car and leave nothing in view: no suitcases, bags or boxes (even empty ones). Better safe than sorry.