Here is a variation of Alex R’s code working with multiple elements

http://jsfiddle.net/XYJEN/1/

function SelectSelectableElements (selectableContainer, elementsToSelect)
{
    // add unselecting class to all elements in the styleboard canvas except the ones to select
    $(".ui-selected", selectableContainer).not(elementsToSelect).removeClass("ui-selected").addClass("ui-unselecting");

    // add ui-selecting class to the elements to select
    $(elementsToSelect).not(".ui-selected").addClass("ui-selecting");

    // trigger the mouse stop event (this will select all .ui-selecting elements, and deselect all .ui-unselecting elements)
    selectableContainer.data("selectable")._mouseStop(null);
}

Update:

jQueryUI 1.10, per comments from kmk: http://jsfiddle.net/XYJEN/163/

Assuming the selectable sample on the jQuery UI website (http://jqueryui.com/demos/selectable/):

<style>
    #feedback { font-size: 1.4em; }
    #selectable .ui-selecting { background: #FECA40; }
    #selectable .ui-selected { background: #F39814; color: white; }
    #selectable { list-style-type: none; margin: 0; padding: 0; width: 60%; }
    #selectable li { margin: 3px; padding: 0.4em; font-size: 1.4em; height: 18px; }
    </style>
    <script>
    $(function() {
        $( "#selectable" ).selectable();
    });
    </script>



<div class="demo">

<ol id="selectable">
    <li class="ui-widget-content">Item 1</li>
    <li class="ui-widget-content">Item 2</li>
    <li class="ui-widget-content">Item 3</li>
    <li class="ui-widget-content">Item 4</li>
    <li class="ui-widget-content">Item 5</li>
    <li class="ui-widget-content">Item 6</li>
    <li class="ui-widget-content">Item 7</li>
</ol>

</div><!-- End demo -->

you can have a function like:

    function selectSelectableElement (selectableContainer, elementToSelect)
    {
        // add unselecting class to all elements in the styleboard canvas except current one
        jQuery("li", selectableContainer).each(function() {
        if (this != elementToSelect[0])
            jQuery(this).removeClass("ui-selected").addClass("ui-unselecting");
        });

        // add ui-selecting class to the element to select
        elementToSelect.addClass("ui-selecting");

        selectableContainer.selectable('refresh');
        // trigger the mouse stop event (this will select all .ui-selecting elements, and deselect all .ui-unselecting elements)
        selectableContainer.data("selectable")._mouseStop(null);
    }

and use it like:

// select the fourth item
selectSelectableElement (jQuery("#selectable"), jQuery("#selectable").children(":eq(3)"));

This can be improved to allow selecting a collection of elements, but it’s a starting point to get you going.

There you go:

,calc: function() { this._mouseStop(); },
custom: function(guys) {
  var self = this;
  self.selectees.removeClass("ui-selected");
  guys.each(function(){
    $(this).addClass("ui-selecting");
    self._trigger("selecting", {}, {
       selecting: this
    });
  });
  this.calc(); // do the selection + trigger selected
} 

Add this after _mouseStop in selectable.js and then you can say:

$("#selectable").selectable("custom", $("#selectable :first-child"));

… or whatever you like.

Have fun! 🙂

Edit : Sorry for the misunderstanding, I’m editing my answer.

So, yes it is possible the selection of the object corresponds to the class ui-selected, so what you can do is :

$(#button).click(function(){
  $("#element1").addClass("ui-selected");

  .......

});

Is it not possible to trigger the selected event manually with .trigger(‘selected’)?

Using Ionut code, how about:

 $("#selectable li:first").trigger('start').trigger('selecting').trigger('selected'); 

?