The material constants are:

modulus of elasticity (E);

weight density (DEN);
Poisson's ratio (POISS);

co-efficient of Thermal Expansion (ALPHA),

Composite
Damping Ratio, and

beta angle (BETA) or coordinates for any reference (REF) point.

E value for members must be provided or the analysis will not be performed.
Weight density (DEN) is used only when selfweight of the structure is to be taken into account.

Poisson's ratio (POISS) is used to calculate the shear modulus (commonly known as G) by the formula,
G = 0.5⋅E/(1 + POISS)

If Poisson's ratio is not provided, STAAD will assume a value for this quantity based on the value of E.

Coefficient of thermal expansion (ALPHA) is used to calculate the expansion of the members if temperature loads are applied. The temperature unit for temperature load and ALPHA has to be the same.
Composite damping ratio is used to compute the damping ratio for each mode in a dynamic solution. This is only useful if there are several materials with different damping ratios.