[Solved]-How to modiffy Highchart size with slide effect-Highcharts

Looks like you need to use the step option of .animate()

    $('#resize').click(function(){
    $('#first').animate({
        width : '100%'
    },{
    duration: 600,
    step: function() {
      $('#first').highcharts().reflow();
    }
    });

    $('#second').animate({
        width : 'toggle',
        opacity : 'toggle'
    }, 600).queue(function(){
        $('#first').highcharts().reflow();
    });
});

Updated Fiddle