The default MUI theme includes a set of shadows that can be used to show varying levels of elevation. These shadows consist of 25 levels, ranging from 0 to 24. UI Foundations Kit uses a small subset of shadows, to enforce a consistent design language across all components. Instead of 25 levels, UI Foundations Kit uses 6 levels of shadows, ranging from a subtle border like shadow to a more pronounced shadow for modals and dialogs. You can see a comparison between the UI Foundations theme and the default MUI theme below:

MUI Shadows

UI Foundation Shadows

This is how it is implemented in the theme file:
theme.ts
shadows: [
  'none',
  '0 1px 2px 0 rgb(0 0 0 / 0.05)', // border-like
  '0 1px 3px rgb(44 42 38 / 7%), 0 4px 16px rgb(44 42 38 / 6%)', // xs
  '0 1px 4px rgb(44 42 38 / 7%), 0 4px 24px rgb(44 42 38 / 7%)', // sm
  '0 4px 6px -1px rgba(0, 0, 0, 0.1), 0 2px 4px -1px rgba(0, 0, 0, 0.06)', // md
  '0 10px 15px -3px rgba(0, 0, 0, 0.1), 0 4px 6px -2px rgba(0, 0, 0, 0.05)', // lg
  '0 20px 25px -5px rgba(0, 0, 0, 0.1), 0 10px 10px -5px rgba(0, 0, 0, 0.04)', // xl
  '0 1px 2px 0 rgb(0 0 0 / 0.05)', // defaults back to the border-like shadow
  '0 1px 2px 0 rgb(0 0 0 / 0.05)',
  // ... continued for all the remaining levels
] as Shadows,
By default, components like the button are already preconfigured to output softer shadows, but you can add shadows to other components as you see fit like this: 
<Paper sx={{
  // the index of the shadow you want to apply
  boxShadow: 3, // '0 1px 4px rgb(44 42 38 / 7%), 0 4px 24px rgb(44 42 38 / 7%)'
}}>
  <Typography variant="h6">Paper with a shadow</Typography>
</Paper>