Here's a reference to it... - the abstract is at the link below along with other abstracts on Mt Rainier.

3-D EDIFICE STABILITY OF MOUNT RAINIER, WA. Mark E. Reid, Dianne L.
Brien, and Thomas W. Sisson, all at USGS, Menlo Park, CA. [GEO]

Massive slope failures have affected the edifice and surrounding valleys of Mount Rainier, and the consequences of future failures may be severe. We use a 3-D slope stability model to examine edifice instability resulting from the interplay between topography, potential failure surfaces, and the 3-D distribution of rock strength. We evaluate the potential for large (> 0.1 km3) gravitationally-induced landslides using three scenarios.

Our initial scenario, using homogeneous rock properties, examines instability induced by topography alone. In this case, the least stable portion of the edifice is predicted in the steep, north-facing Willis Wall, an area where few large landslides have originated.

Our second scenario incorporates variations in strength caused by the hydrothermal alteration of volcanic rocks. Using geologic mapping, we divide the edifice into four units: strong basement rocks; relatively strong, fresh volcanic flows and breccias; slightly weaker, lightly altered rocks; and weak, highly altered rocks. In this scenario, the west-facing Sunset Amphitheater is predicted as the least stable; many past failures have originated from this area.

In our third scenario we build on the second scenario by adding the 3-D geologic complexity of the large subsurface Osceola failure scar, where newer volcanic rocks overlie older altered rocks. This model predicts some reduced stability of the eastern flank, although the overall least stable region is still the Sunset Amphitheater area.
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I guess its like anything else - some say the east is weaker and some say the north is weaker -
Here's another reference from http://mt.rainier.tribnet.com/geology/geo1.asp :

“It’s not going to surprise geologists if the whole thing lets go,” he said.

He has also singled out Rainier’s most vulnerable spots – the places that are most likely to
crumble next.

The mountain’s west side is the worst: From Sunset Amphitheater to Puyallup Cleaver and down the Puyallup River drainage, the rock is very rickety. The east side is nearly as bad, leading into the White River drainage. The area above the Cowlitz River is relatively solid.

The patterns of weakened rock reflect the mountain’s inner plumbing. Sheet-like fractures in the
rock, oriented east and west, channel acidic water through the edifice.

The pattern also points up the areas most vulnerable to future mudflows: the Puyallup, White and Nisqually rivers.

“There are clearly higher-risk areas and lower-risk areas,” Zimbelman said.

An independent researcher who sometimes works for the federal government, Zimbelman
criticizes the Geological Survey for failing to point out these differences in the hazard maps it
prepares for surrounding communities. The maps assume the risk of mudflows is roughly comparable in all of the valleys leading from Mount Rainier.

Better safe than sorry, is the agency’s stance.

While it’s true that some drainages are more hazardous than others, it’s also true that all of the
valleys have been hit by mudflows, said Scott, who prepared the maps.

• Mount Rainier National Park - 100th Anniversary Symposium - Geology session