Full Width Material-UI Grid not working as it should

I suspect the Container component is causing you problems. Since you haven’t linked its implementation, see below for a working example of what you want.

Since Material uses flexbox they make use of property flexGrow

The flex-grow CSS property specifies the flex grow factor of a flex item. It specifies what amount of space inside the flex container the item should take up. The flex grow factor of a flex item is relative to the size of the other children in the flex-container.

This is the property that governs the growth of elements in the grid.

import React from 'react';
import PropTypes from 'prop-types';
import { withStyles } from 'material-ui/styles';
import Paper from 'material-ui/Paper';
import Grid from 'material-ui/Grid';

const styles = theme => ({
  root: {
    flexGrow: 1,
  },
  paper: {
    padding: theme.spacing.unit * 2,
    textAlign: 'center',
    color: theme.palette.text.secondary,
  },
});

function CenteredGrid(props) {
  const { classes } = props;

  return (
    <div className={classes.root}>
        <Grid container spacing={24}>
          <Grid item xs={12} sm={6}>
            <Paper>xs=12 sm=6</Paper>
          </Grid>
          <Grid item xs={12} sm={6}>
            <Paper>xs=12 sm=6</Paper>
          </Grid>
        </Grid>
    </div>
  );
}

CenteredGrid.propTypes = {
  classes: PropTypes.object.isRequired,
};

export default withStyles(styles)(CenteredGrid);