Non-destructive stress tests are currently being carried out on Southwest's fleet of Boeing 737.
The US National Transportation Safety Board says it is aware of "crack indications in the lap joints" on the fuselage on three aircraft so far.
Southwest Airlines estimates around 100 flights will be cancelled from its Monday (April 4) schedule due to the inspections. Approximately 300 were cancelled over the weekend.
The airline says the aircraft inspections are due for completion by late-Tuesday (April 5).
Southwest Airlines is inspecting 81 of its Boeing 737 aircraft after a hole mysteriously appeared in the roof of the fuselage during a flight in the US.
The low cost carrier made an emergency landing in the Arizona town of Yuma shortly after part of the roof ripped open and cabin pressure inevitably plummeted on the flight from Phoenix, Arizona, to Sacramento in California.
Apart from the obvious shock and distress amongst passengers, there were actually only a few minor injuries (including one crew member) and no transfers to hospital were required, Southwest says.
Most passengers boarded another aircraft a few hours later to complete the journey. The crew has been praised by many passengers for its handling of the incident.
But this being 2011, social media has played a huge part in the saga - from the running commentary of the incident in its early stages to feedback and analysis now that Southwest has decided to ground dozens of its aircraft.
And, once again, it looks like Southwest is playing the whole thing extremely well, despite the obvious concerns around, err, a hole appearing in the roof of one of its aircraft mid-flight.
At the centre of coverage in social media is doctoral student Shawna Malvini Redden, who managed to snap some incredible photos during the incident and upload them within minutes to Twitpic.
Malvini Redden has, inevitably, become an overnight star, appearing on shows such as Good Morning America, Fox, MSNBC, Associated Press, WSJ radio, CBS and Geraldo.
As so often happens when an individual also becomes part of the incident, Southwest has not attempted to muzzle any element of her story and appears content to watch it all play out in the mainstream and social media.
This is clearly a wise action, but clearly not the tactic some corporations would use when faced with overwhelming coverage, much of it negative (yes, the aircraft landed safely - but it still managed to find itself with a hole in the roof mid-flight).
The airline's messages on Twitter have been calmed and, most importantly, informative.
Even on its Facebook page, which has a massive 1.35 million fans, Southwest has simply let the commentary and analysis (some of it somewhat hysterical) run and run rather than simply - and easily - deleting some of the comments.
Southwest has taken this measured and sensible approach to social media before, when comedian and director Kevin Smith turned on the airline in early 2010 after a rather unfortunateseating incident.
Travel companies (any company, for that matter) cannot control the conversation that takes place in social media. But Southwest has shown again how to handle a situation that clearly has some negative impact on the brand, by appearing to let the chatter which it can conceivably control (on Facebook) take its course and watch on the sidelines while the rest of the analysis plays out publicly.